20 + 5(15 7) 5 2. = 15 2(10) 4 (3 3) = = = = 2(9 + 3) 6 = 2(12) 6. You try: 1 Simplify 15 2(3+ 7)

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1 Simplify (+ 7) (0) ( ) AF./.EE. a) Simplify b) Evaluate: ( 7). Evaluate: ac ( + ) ( b ) when a, b, and c. ac ( + ) ( b ) ( + ) ( ) ( + ) (9 + ) ().0/.EE.c ) Evaluate: ca ( ) ( b a) when a, b, and c. Simplify: " 9 $ % ' # 9& " 8 $ % ' # 8& ) Simplify: NS./7.NS.c Page of 9 MCC@WCCUSD (HUSD) /0/

2 Simplify the expressions: a) b) b b b b + 7 c) d) ( x y) x y 9 x 0 y 8x 0 y Simplify ( xy) ( xy ). ( xy)( xy) xy OR ( xy) x x y y ( x ) y x y xy y z y z y z x y xy x y x y x y.0/8.ee..0/8.ee. Simplify the expressions: ) n n n ) xy x y ) x y 7) ( x y) 8) 9) 8 0x y x y z (a b 8 )(a b ) a b 0) Simplify (xy ). Page of 9 MCC@WCCUSD (HUSD) /0/

3 Simplify 8 mn 9mn m n 9 mn m n mn 9mn /8.EE. Simplify. ) ) x 7 x m n m n 7 Simplify ) Simplify 0..0/8.EE. 8 Write an equation that describes the following statement: less than a number is 8. Less than indicates subtraction and any variable can represent the unknown number. Therefore, the answer is: x 8 AF./A.REI. 8 Write an expression that describes each of the following: ) Four subtracted from a number ) Seven times a number squared Page of 9 MCC@WCCUSD (HUSD) /0/

4 9 Solve: a) x+ x+ x+ x+ x x 9 Solve. a) x x! +!!!!! 0!!! x" x! x! x! x!! b) y 9 7y!!!!!!! c) x ( x+ ) b) Solve: x x.0/a.rei. Page of 9 MCC@WCCUSD (HUSD) /0/

5 0 Solve and graph: x > 7x+ 0 x > 7x+ x > x+ x+ > x + > x + 8> x > x x > 7x+ x 7x> 7x 7x+ x > x + > + x > 8 x > 8 8 x < x < Solve and graph: 7a) x + 9 7b) 0 > ( x ) Graph : Negative is greater than x x <.0/A.REI.,.EE.8 Solve: ( x ) (x ) 0 x 0 x+ 0 x x x 8 0 x x 8 x 8 x 8 8) Solve. 8x (x+ 8) 7x.0/A.REI. Page of 9 MCC@WCCUSD (HUSD) /0/

6 Write an equation for a line that passes through the points (,) and(,). y mx + b wherem is the slope and b is the y-coordinate of the y-intercept. 9) Write an equation for a line that passes through the points(,7)and(,). ( xy, ) (,) (, ) m slope rise run ( ) + y mx+ b () + b b + b b or y y m( x x ) y ( x ( )) y ( x+ ) 8 y x+ 8 y x+ Therefore, the equation of the line is y x + 7.0/8.F. Page of 9 MCC@WCCUSD (HUSD) /0/

7 Graph x y 8 Graph means plot a point for all of the solutions. Since the equation is written in standard form find the x and y intercepts: x y 8 (0) y 8 0 y 8 y 8 y 8 y One solution is(0,). Similarly, if we substitute 0 for y, we ll get(,0). And (,) is a solution. If we continue to choose all numbers for x, the solutions form a line. 0) Graph x+ y.0,7.0/f.if.7a Page 7 of 9 MCC@WCCUSD (HUSD) /0/

8 Write the equation of the line passing through the point(,) and parallel to the line y x. The line parallel to the line y x will have the same slope which is m. ) Write the equation of the line passing through the point(, ) and parallel to the line y x+. y x+ b ( ) + b + b b OR y ( x ( )) y ( x+ ) y x The equation is y x. 8.0/G.GPE. What is the slope of a line perpendicular to y x? The slope of y x is. The slope of a line perpendicular to y x is the opposite reciprocal of. That is, ) What is the slope of a line perpendicular to y x+? 8.0/G.GPE. Page 8 of 9 MCC@WCCUSD (HUSD) /0/

9 Graph x + y 9 by finding the x-intercept and y-intercept. The x-intercept is where the graph crosses the x- axis. The graph crosses the x-axis when y 0. Let y 0 x+ y 9 x x x x-intercept is,0 Let x 0 x+ y 9 0+ y 9 0+ y 9 y y-intercept is 0, ) Graph the linear equation by finding the x- and y-intercepts: + y 7 Find the domain and range for the set of ordered pairs. Then tell if the relation is a function. {(,),(8, ),(, ),(,)} Domain: {,8,} Range: {,,,}.0/F.IF.7 This is not a function because the x- coordinate is paired with two different y- coordinates 7.0/F.IF. 7 ) Find the domain and range for the given relation. Then tell if the relation is a function. {(,),(,),(0, 7),(,8)} Page 9 of 9 MCC@WCCUSD (HUSD) /0/

10 8 Solve the system x y by graphing. y x Graph x y by finding intercepts. a. Use a table to find the intercepts. x x y y 0 0 y y ( y) ( ) y x 0 0 x b. Plot the intercepts (0,) and (,0). c. Graph the line. (see graph below) Now, graph y x using slope-intercept form y mx + b. 8 Solve the system of equations by graphing. Check your solution algebraically by substituting the ordered pair in each equation to make sure it gives you a true statement in each equation. ) x + y y x + a. Identify the slope m b. Identify the y-intercept 0, c. Plot ( 0, ), go down two units and right one unit and plot a point. Graph the line. Then, locate the point of intersection of the lines. is the solution to the system, x y check algebraically! y x 9.0/A.REI. Page 0 of 9 MCC@WCCUSD (HUSD) /0/

11 9 Solve the system: x+ y x+ y Using the Substitution Method, Solve the first equation for y : Eq: x+ y y x 9 ) Solve the system using the substitution method: x y y Substitute for y in the second equation: Eq: x+ y x+ ( x) x+ x x + x x Substitute for x in either equation: Eq: x+ y () + y y y The solution is(, ). 9.0/A.REI. Page of 9 MCC@WCCUSD (HUSD) /0/

12 0 x y Solve the system + y by the elimination method. Make the coefficients of the y-terms opposites by multiplying the first equation by and the second equation by : 0 7) Solve the system using the elimination method: x 7y x y (x y) () (+ y) () 8x y 0 + y By the Addition Property of Equality 8x y+ (+ y) 0 + () 8x+ y+ y x x x Substitute for x in either equation x y () y 8 y y 8 y y the solution is(,). 9.0/A.REI. End of Study Guide Page of 9 MCC@WCCUSD (HUSD) /0/

13 You Try Solutions: a) Simplify: 0 ( 7) 0 + (8) b) Evaluate: 9 + ) Simplify: Simplify: ) n n n n ++ n 8 ) xy x y ) Evaluate: ca ( ) ( b a) a, b, and c. ca ( ) ( b a) if ( ) x + y + x y ) x y x y x x y y 7) ( x y) x y ( 8) x y x y Page of 9 MCC@WCCUSD (HUSD) /0/

14 You try continued: 8) 0x 8 y x y z x8 y z x y z y z Simplify ) x x 7 x 7 x xixixixixixix xixix x x 7 x x 7 x 9) (a b 8 )(a b ) a b a+ b 8+ a b a7 b 0 a b a 7 b 0 a b ) mn mn m n m n i9imimimimiminin i imimininininin 9m n m n m n i9im in i 9m n 9m n 0) Simplify ( xy ). 7 (xy ) ( xy ) xy iixixi y i y x y 0 (xy ) ( x) ( y ) x i y i x y 0 ) Simplify 0. 9 Page of 9 MCC@WCCUSD (HUSD) /0/

15 8 Write an expression that describes each of the following: ) Four subtracted from a number x ) Seven times a number squared 7y 9 Solve. x a) + 7 x x 8! # " x $ &! i$ # & % " % x b) y 9 7y y y+ y y + + y+ y+ y y y 9 7y y 9 y 7 y y 9 y 9 + y + y y c) x ( x+ ) x + x x+ ( x ) x+ x+ + x x+ x+ x x x+ x x ( x ) x + x x 0 x + x x 0 + x x 0 x 8 x 8 8 x x Page of 9 MCC@WCCUSD (HUSD) /0/

16 0 Solve and graph: 7a) x + 9 x + 9 x + 9 x x 0 0 x x 0 7b) 0 > ( x ) 0 > x 0 > x + 0 > x + 0 > x + > x ii7 i > x 7 > x 9) Write an equation for a line that passes through the points(,7)and(,). ( xy, ) (,7) (,) y mx+ b 7 + b b b + b m slope rise run 7 y y m( x x ) y ( x ) y x+ ( ) 8 y + x+ + y x+ Therefore, the equation is of the line is y x ) Solve. 8x (x+ 8) 7x 8x (x+ 8) 7x 8x x 7x x 0 x+ 0 x Page of 9 MCC@WCCUSD (HUSD) /0/

17 0) Graph x+ y Finding the intercepts: Let y 0 Let x 0 x+ y x+ y x + 0 x + 0 x x,0 x-intercept is 0+ y 0+ y y y-intercept is ( 0, ) OR rewriting in slope-intercept form: ) Write the equation of the line passing through the point(, ) and parallel to the line y x+ Parallel lines have the same slope and different y-intercepts. m y mx + b y y m x x + b y ( ) ( x ) + b y+ x 8 b y x 8 Equation of the line is y x 8 x+ y x+ y+ x + x y x+ y x + y x+ ) What is the slope of a line perpendicular to y x +? Slope of y x + is. The slope of the line perpendicular to y x + is the opposite reciprocal of. That is,. Page 7 of 9 MCC@WCCUSD (HUSD) /0/

18 8 Solve the system of equations by graphing. ) Graph the linear equation by finding the x- and y-intercepts: + y Graph the linear equation by finding the x- and y-intercepts: + y Let y 0 + y x x-intercept is,0 Let x 0 + y 0 + y 0 + y y y-intercept is 0, Check your solution algebraically by substituting the ordered pair in each equation to make sure it gives you a true statement in each equation. ) x + y y x + Graph x + y by finding intercepts. x x + y y y y x + 0 y 0 Plot the intercepts ( 0, ) and (, 0) Graph the line. (see graph below) Now, graph y x + using slope-intercept form. The slope is and the y-intercept is. 7 ) Find the domain and range for the given relation. Then tell if the relation is a function. {(,),(,),(0, 7),(,8)} Domain: {,, 0, } Range: {,, 7,8} Yes, the relation is a function since every input value is assigned to exactly one output value. The solution to the system is the point of intersection of the graphs which is ( 9, ). Remember to check the solution algebraically. Page 8 of 9 MCC@WCCUSD (HUSD) /0/

19 9 0 ) Solve the system using the substitution method: 7) Solve the system using the elimination method: x y y To solve using substitution we need to isolate a variable for one of the equations. Isolate y in equation. x 7y x y Choose a variable to eliminate. Make the coefficients of the variables opposites by multiplying one or both equations. Eliminating the x-terms: Eq : x y x y + y + y x y + x y + x y Substitute x for y into Eq and solve. Eq : y (x ) x+ x + + x + 0 x+ x+ 0+ x x Substitute x into either equation and solve for y. x y y 9 y 7+ y 7 y 0 7 y+ y 0+ y 7 y The solution to the system is (, 7 ). Eq: Eq : ( x y) ( x y) 7 Adding vertically: x y 9 x+ y 0x 7 y 7 7 y 7 y Substitute y into either equation and solve for x x 7y x 7 x 7 x x 0 x,. The solution to the system is x y 9 x+ y Page 9 of 9 MCC@WCCUSD (HUSD) /0/