Practice Test - Chapter 6 Graph each system and determine the number of solutions that it has. If it has one solution, name it. 1. y = 2x y =6 −x SOLUTION: To graph the system, write both equations in slopeintercept form. y = 2x y = −x + 6
The solution is (2, 4). 2. y = x − 3 y = −2x + 9 SOLUTION: y=x−3 y = −2x + 9
The graph appears to intersect at the point (4, 1). You can check this by substituting 4 for x and 1 for y.
The graph appears to intersect at the point (2, 4). You can check this by substituting 2 for x and 4 for y.
The solution is (4, 1). 3. x − y = 4 x + y = 10
The solution is (2, 4). 2. y = x − 3 y = −2x + 9 SOLUTION: y=x−3 y = −2x + 9
SOLUTION: To graph the system, write both equations in slopeintercept form. Equation 1:
Equation 2:
Graph and solve. y=x−4 y = −x + 10
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at the point (4, 1). You can check this by substituting 4 for x and 1 for y.
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Practice Test - Chapter 6 The solution is (4, 1). 3. x − y = 4 x + y = 10 SOLUTION: To graph the system, write both equations in slopeintercept form. Equation 1:
The solution is (7, 3). 4. 2x + 3y = 4 2x + 3y = −1 SOLUTION: To graph the system, write both equations in slopeintercept form. Equation 1:
Equation 2: Equation 2:
Graph and solve. y=x−4 y = −x + 10
Graph and solve.
The graph appears to intersect at the point (7, 3). You can check this by substituting 7 for x and 3 for y.
The lines are parallel. So, there is no solution.
Use substitution to solve each system of equations. 5. y = x + 8 2x + y = −10 The solution is (7, 3). 4. 2x + 3y = 4 2x + 3y = −1 SOLUTION: To graph the system, write both equations in slopeintercept form. Equation 1:
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Equation 2:
SOLUTION: y=x+8 2x + y = −10 Substitute x + 8 for y in the second equation.
Page 2 Use the solution for x and either equation to find the value for y.
Practice Test - Chapter 6 The lines are parallel. So, there is no solution. Use substitution to solve each system of equations. 5. y = x + 8 2x + y = −10 SOLUTION: y=x+8 2x + y = −10 Substitute x + 8 for y in the second equation.
The solution is (−6, 2). 6. x = −4y − 3 3x − 2y = 5 SOLUTION: x = −4y − 3 3x − 2y = 5 Substitute −4y − 3 for x in the second equation.
Use the solution for x and either equation to find the value for y.
The solution is (−6, 2). 6. x = −4y − 3 3x − 2y = 5 SOLUTION: x = −4y − 3 3x − 2y = 5 Substitute −4y − 3 for x in the second equation.
Use the solution for y and either equation to find the value for x.
The solution is (1, −1). 8. MULTIPLE CHOICE Use elimination to solve the system. 6x − 4y = 6 −6x + 3y = 0 A (5, 6) B (−3, −6) C (1, 0) D (4, −8) SOLUTION: Because 6x and −6x have opposite coefficients, add the equations.
Use the solution for y and either equation to find the value for x.
Now, substitute −6 for y in either equation to find the value of x.
The solution is (1, −1). eSolutions Manual - Powered by Cognero
8. MULTIPLE CHOICE Use elimination to solve the system.
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Practice Test - Chapter 6 The solution is (1, −1). 8. MULTIPLE CHOICE Use elimination to solve the system. 6x − 4y = 6 −6x + 3y = 0 A (5, 6) B (−3, −6) C (1, 0) D (4, −8)
The solution is (−3, −6). So, the correct choice is B. Use elimination to solve each system of equations. 10. x + y = 13 x −y = 5 SOLUTION: Because y and −y have opposite coefficients, add the equations.
SOLUTION: Because 6x and −6x have opposite coefficients, add the equations.
Now, substitute 9 for x in either equation to find the value of y.
Now, substitute −6 for y in either equation to find the value of x.
The solution is (9, 4). 11. 3x + 7y = 2 3x − 4y = 13
The solution is (−3, −6). So, the correct choice is B. Use elimination to solve each system of equations. 10. x + y = 13 x −y = 5 SOLUTION: Because y and −y have opposite coefficients, add the equations.
SOLUTION: Because 3x and 3x have the same coefficients, multiply equation 2 by −1, then add the equations.
Add the equations.
Now, substitute −1 for y in either equation to find the value of x.
Now, substitute 9 for x in either equation to find the value of y.
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The solution is (3, −1).
Practice Test - Chapter The solution is (9, 4). 6 11. 3x + 7y = 2 3x − 4y = 13 SOLUTION: Because 3x and 3x have the same coefficients, multiply equation 2 by −1, then add the equations.
Add the equations.
Now, substitute −1 for y in either equation to find the value of x.
The solution is (3, −1). 12. x + y = 8 x − 3y = −4 SOLUTION: Because x and x have the same coefficients, multiply equation 2 by –1 and then add the equations.
The solution is (3, −1). 12. x + y = 8 x − 3y = −4 SOLUTION: Because x and x have the same coefficients, multiply equation 2 by –1 and then add the equations.
Add the equations.
Now, substitute 3 for y in either equation to find the value of x.
The solution is (5, 3). 13. 2x + 6y = 18 3x + 2y = 13 SOLUTION: Multiply the second equation by −3.
Now, because 6y and −6y have opposite coefficients, add the equations.
Add the equations.
Now, substitute 3 for y in either equation to find the value of x. eSolutions Manual - Powered by Cognero
Now, substitute 3 for x in either equation to find the value of y.
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Practice Test - Chapter 6 The solution is (5, 3). 13. 2x + 6y = 18 3x + 2y = 13 SOLUTION: Multiply the second equation by −3.
Now, because 6y and −6y have opposite coefficients, add the equations.
Now, substitute 3 for x in either equation to find the value of y.
The solution is (3, 2). Determine the best method to solve each system of equations. Then solve the system. 15. y = 3x x + 2y = 21 SOLUTION: y = 3x x + 2y = 21
Substitute 3x for y in the second equation.
Use the solution for x and either equation to find the value for y.
The solution is (3, 2). Determine the best method to solve each system of equations. Then solve the system. 15. y = 3x x + 2y = 21 SOLUTION: y = 3x x + 2y = 21
Substitute 3x for y in the second equation.
The solution is (3, 9). 16. x + y = 12 y =x−4 SOLUTION: y=x–4 x + y = 12 Substitute x – 4 for y in the second equation.
Use the solution for x and either equation to find the value for y.
Use the solution for x and either equation to find the value for y.
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The solution is (8, 4).
Practice Test - Chapter The solution is (3, 9). 6 16. x + y = 12 y =x−4 SOLUTION: y=x–4 x + y = 12 Substitute x – 4 for y in the second equation.
The solution is (12, 3). 18. 3x + 5y = 7 2x − 3y = 11 SOLUTION:
Because none of the terms are opposites, use elimination by multiplication to solve. Multiply the first equation by 2 and the second equation by -3. Then add the equations to eliminate the x-term. 3x + 5y = 7 2x − 3y = 11
Use the solution for x and either equation to find the value for y.
The solution is (8, 4). 17. x + y = 15 x −y = 9 SOLUTION: Because the y-terms have opposite coefficients, add the equations.
Substitute -1 for y in the second equation to find x.
The solution is (4, –1). Now, substitute 12 for x in either equation to find the value of y.
The solution is (12, 3). 18. 3x + 5y = 7 2x − 3y = 11 SOLUTION: eSolutions Manual - Powered by Cognero
Because none of the terms are opposites, use elimination by multiplication to solve. Multiply the
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