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Name _____________________________ Systems of Equations Study Island Copyright © 2014 Edmentum - All rights reserved. 4. Use elimination to find the solution to the system of equations. 1. -3x - 4y = -24 -2x + 4y = 4 A. Find the solution to the system of equations shown above by graphing. A. x = 5, y = 3 B. B. x = 4, y = 4 C. x = 3, y = 4 D. x = 4, y = 3 C. D. 2. 5. Find the solution to the system of equations given below using elimination by addition. Using the two equations above, solve for y. A. B. C. A. B. D. C. 3. Describe the solution to the system of equations below. The system has infinitely many solutions of the form y = 5x - 8, where x is any real A. number. B. C. D. The system has the unique solution (-6, -38). The system has the unique solution (4, 12). The system has no solution. D. Name _____________________________ 6. Systems of Equations 9. Describe the solution to the system of equations graphed below. 2x + y = -4 6x + 3y = -12 A. B. C. D. 7. A. The system has no solution. B. The system has the unique solution (2, 2). A. C. The system has the unique solution (3, 12). B. The system has infinitely many solutions of D. the form y = -2x - 4 where x is any real number. C. D. 10. Use elimination to find the solution to the system of equations. 8. Find the solution to the system of equations given below using elimination by addition. 3x + 15y = 30 x + 3y = 6 A. B. C. D. A. x = -12, y = 6 B. x = 24, y = -6 C. x = 12, y = -2 D. x = 0, y = 2 Name _____________________________ Systems of Equations Answers 1. D 2. A 3. D 4. D 5. D 6. D 7. C 8. D 9. D 10. D Now, substitute x into the first equation. Explanations 1. Graph each equation on the coordinate plane. The point of intersection of the two graphs gives the solution to the system of equations. 3. One way to solve a system of equations is to graph the equations, and find the point of intersection. Start by placing both equations in slope-intercept form. Notice that both equations have the same slope but different y-intercepts. The two lines are parallel and will never intersect. Thus, the system has no solution. 4. Use elimination by addition to solve the system of equations. The two lines intersect at (4, 3). So, x = 4 and y = 3 is the solution. 2. First, solve the second equation for x. Start by eliminating the y-terms, and then solve for x. Name _____________________________ Next, substitute x = 3 into one of the original equations and solve for y. Systems of Equations 7. 8. Use elimination by addition to solve the system of equations. 3x + 15y = 30 x + 3y = 6 Therefore, the solution to the system of equations is x = 3, y = 1. 5. Use elimination by addition to solve the system of equations. Start by eliminating the x term. To do this, multiply the second equation by -3, and then add the two equations together. 3x + 15y = 30 -3x - 9y = -18 Start by eliminating the y term. To do this, multiply the first equation by -5, and then add the two equations together. Next, substitute x = -9 into the first equation, and solve for y. 6y = 12 y= 2 Next, substitute y = 2 into the original second equation, and solve for x. x + 3y = 6 x + 3(2) = 6 x+6=6 x=6-6 x=0 Therefore, the solution to the system of equations is x = 0, y = 2. 9. Notice that there is only one line graphed and when solved for y, both equations have the same slope and the same y-intercept. The two equations graph the same line that will intersect at infinitely many points. Therefore, the solution to the system of equations is . 6. Thus, the system has infinitely many solutions of the form y = -2x - 4 where x is any real number. 10. Use elimination by addition to solve the system of equations. Start by eliminating the y-terms, and then solve for x. Name _____________________________ Next, substitute x = 3 into one of the original equations and solve for y. Therefore, the solution to the system of equations is x = 3, y = -6. Systems of Equations