Graphing and Elimination Review for Quiz: Sections 5.1 and 5.3 Solving Systems by Graphing and Elimination

{ Solve the system of equations by graphing: y = 2x – 8 y = x 3 + 0 Graph the first line:  y-intercept: 8 on y-axis  use slope = 2 = 2 up 1 right Graph the second line:  y-intercept: 0 on y-axis  use slope = 2 up 3 right Solution: (6, 4)

{ 2. Solve the system of equations by graphing: y = – x + 6 4 5 Graph the first line: 5 5 5  y-intercept: 6 on y-axis  use slope = 4 down 5 right Graph the second line:  Solve the equation for y. y = – x – 4 4 5  y-intercept:  4 on y-axis Solution: no solution  use slope = 4 down 5 right

{ 3. Solve the system of equations by graphing: y = x – 2 x – 3y = 6 1 3 Graph the first line:  y-intercept: 2 on y-axis.  slope = 1 up 3 right Graph the second line:  Solve the equation for y. 1 x  3y = 6 Give y a positive coefficient. 1x + 3y = 6 +1x +1x 3y = 1x  6 Solution: infinite solutions 3 3 3 y = x  2 1 3 Same as first equation.

{ 4. Solve the system of equations by graphing: x = –3 2x + 3y = 12 Graph the first line:  x is always 3. x y 3 0 3 1 3 2 Graph the second line:  Solve the equation for y. 2x + 3y = 12 y has a positive coefficient. 2x 2x 3y = 2x + 12 y-intercept: 4 on y-axis Solution: (3, 6) 3 3 3 y = x + 4 2 3 2 down 3 right slope =

{ 5. Solve the system of equations by elimination: 3x – 4y = 38 Add the equations: 8x = 16  The variable y cancels out. 8 8  Solve for x. x = 2 Solve for the 2nd variable: 5x + 4y = 22 5(2) + 4y = 22  Substitute x into either equation. 10 + 4y = 22  Solve for y. –10 –10 4y = 32 Solution: in alphabetical order. 4 4 Solution: (2, –8) y = 8

{ 6. Solve the system of equations by elimination: 6x + 5y = 39 Add the equations: 4y = 12  The variable x cancels out. 4 4  Solve for y. y = 3 Solve for the 2nd variable: 6x + 5y = 39 6x + 5(3) = 39  Substitute y into either equation. 6x + 15 = 39  Solve for x. –15 –15 6x = 24 Solution: in alphabetical order. 6 6 Solution: (–4, 3) x = 4

{ 7. Find two numbers whose sum is 26 and whose difference is 14. x + y = 26 x – y = 14 1x + y = 26 1x – y = 14 Write a system of equations: Add the equations: 2x = 40  The variable y cancels out. 2 2  Solve for x. x = 20 Solve for the 2nd variable: x + y = 26  Substitute x into either equation. 20 + y = 26  Solve for y. –20 –20 Solution: y = 6 The numbers are 20 and 6.

{ 8. Solve the system of equations by elimination: 2x + 7y = 53 - - + - - + Nothing cancels out yet : 4x = 36  Take the opposite of either row. 4 4 Add the equations: x = 9  The variable y cancels out.  Solve for x. 2x + 7y = 53 Solve for the 2nd variable: 2(9) + 7y = 53 18 + 7y = 53  Substitute x into either equation. +18 +18  Solve for y. 7y = 35 Solution: in alphabetical order. 7 7 Solution: (–9, –5) y = 5

{ 9. Solve the system of equations by elimination: 6x + 7y = 28 + - + Nothing cancels out yet : 5y = 10  Take the opposite of either row. 5 5 Add the equations: y = 2  The variable x cancels out.  Solve for y. 6x + 7y = 28 Solve for the 2nd variable: 6x + 7(2) = 28 6x + 14 = 28  Substitute y into either equation. 14 14  Solve for x. 6x = 42 Solution: in alphabetical order. 6 6 Solution: (7, 2) x = 7

{ 10. Solve the system of equations by elimination: 11x – 12y = 13 - + + Nothing cancels out yet : 0 = 26  Take the opposite of either row. False Add the equations:  The variables x and y both cancel out. Find the solution.  False Statement: No Solution Solution: No Solution