Mathematics
skaggsm
39

1. Which of the following equations could be the result of using the comparison method to solve the system shown? x + y = 5 2x + y = 7 2. For the following system, use the second equation to make a substitution for y in the first equation. 2x + y = 6 y = 3x + 4 What is the resulting equation? 3. Solve the following system of equations by the substitution method. 10x + 10y = 1 x = y - 3 What is the value of y? 4.Which of the following would not be the result of a substitution in the following system? 2x + y = 7 y - x = 1 5.Solve the following system of equations by the substitution method. x - y = 0 x - y - 2 = 0 What is the solution set? 6. Solve the following system of equations by the substitution method. 8x = 2y + 5 3x = y + 7 What is the solution set? 7.Based on the lesson, which of the following would be the best approach for solving this system by substitution? 5x = y + 6 2x - 3y = 4 8.Which of the following equations could be the result of using the comparison method to solve the system shown? x + 2y = 6 x - 4y = 8 9. Solve the following system of equations. 2x + y = 3 x = 2y - 1 10. For the following system, use the second equation to make a substitution for y in the first equation. 3x + y = 1 y + 4 = 5x What is the resulting equation? 11. For the following system, use the second equation to make a substitution for x in the first equation. x + 5y - 10 = 0 x = 2y - 8 What is the resulting equation in simplest form? 12. For the following system, use the second equation to make a substitution for x in the first equation. 3x + 2y = 7 x - y + 3 = 0 What is the resulting equation? 13. Solve the following system by the comparison method. 2p + q = 1 9p + 3q + 3 = 0 What is the solution set? 14.Which of the following equations could be the result of using the comparison method to solve the system shown? x - 4y - 1 = 0 x + 5y - 4 = 0 15.Solve the following system of equations. 3x + 2y - 5 = 0 x = y + 10

+3
(1) Answers
ItssHannahh

Q1. The answer is 5 - x = 7 - 2x The steps of the comparison methods are: 1. Solve y in the terms of x. 2. Equal y from the both equations. Step 1. x + y = 5 y = 5 - x ______ 2x + y = 7 y = 7 - 2x ... Step 2. y = 5 - x y = 7 - 2x Therefore: 5 - x = 7 - 2x Q2. The answer is 2x + (3x + 4) = 6 Let's simply substitute y from the second equation into the first on: 2x + y = 6 y = 3x + 4 _______ 2x + (3x + 4) = 6 Q3. The answer is 31/20. Let's substitute x from the second equation into the first equation: 10x + 10y = 1 x = y - 3 _________ 10(y - 3) + 10y = 1 10 * y - 10 * 3 + 10y = 1 10y - 30 + 10y = 1 10y + 10y = 30 + 1 20y = 31 y = 31/20 Q4. Since there are no choices, the results of a substitution: 2x + x + 1 = 7 and 2(y - 1) + y = 7 so find out, which one is incorrect among your choices There are two results of the substitution - one solved for x in the terms of y and one solved for y in the terms of x. 2x + y = 7             y - x = 1 _______ 2x + y = 7 x = y - 1 _______ 2(y - 1) + y = 7 2x + y = 7             y - x = 1 _______ 2x + y = 7 y = x + 1 _______ 2x + x + 1 = 7 Q5. The answer is: ∅ (empty set) Let's substitute y from the first equation into the second one: x - y = 0 x - y - 2 = 0 __________ y = x x - y - 2 = 0 __________ x - x - 2 = 0 x - x = 2 0 = 2 Therefore, the solution is an empty set (∅). Q6. The answer is (-9/2, -41/2) Let's solve y in the terms of x in the second equation and substitute y in the first equation: 8x = 2y + 5 3x = y + 7 ________ 8x = 2y + 5 y = 3x - 7 ________ 8x = 2(3x - 7) + 5 8x = 2*3x - 2*7 + 5 8x = 6x - 14 + 5 8x - 6x = -14 + 5 2x = -9 x = -9/2 y = 3x - 7 x = -9/2 ________ y = 3 * (-9/2) - 7 y = -27/2 - 7*2/2 y = -27/2 - 14/2 y = (-27 - 14)/2 y = -41/2 Q7. There are no choices, but the best method would be the substitution method and solving the first equation for y: 5x = y + 6 2x - 3y = 4 ________ y = 5x - 6 2x - 3y = 4 ________ 2x - 3(5x - 6) = 4 And from here it is easy to calculate x and then y. Q8. There are no choices, but the resulting equation is 6 - 2y = 4y + 8.  Let's solve both equations for x and equal them: x + 2y = 6 x - 4y = 8 _______ x = 6 - 2y x = 4y + 8 ______ 6 - 2y = 4y + 8 Q9. The answer is: x = 1, y = 1 Let's substitute x from the second equation into the first one: 2x + y = 3 x = 2y - 1 ________ 2(2y - 1) + y = 3 2 * 2y - 2 * 1 + y = 3 4y - 2  + y = 3 4y + y = 3 + 2 5y = 5 y = 5/5 y = 1 x = 2y - 1 y = 1 _________ y = 2 * 1  - 1 y = 2 - 1 y = 1 Q10. The answer is 3x + 5x - 4 = 1 Use the second equation to make a substitution for y in the first equation: 3x + y = 1 y + 4 = 5x ______ 3x + y = 1 y = 5x - 4 _______ 3x + (5x - 4) = 1 3x + 5x - 4 = 1 Q11. The answer is 7y - 18 = 0 Use the second equation to make a substitution for x in the first equation. x + 5y - 10 = 0 x = 2y - 8 __________ (2y - 8) + 5y - 10 = 0 2y - 8 + 5y - 10 = 0 2y + 5y - 8 - 10 = 0 7y - 18 = 0 Q12. The answer is 3(y - 3) + 2y = 7 Use the second equation to make a substitution for x in the first equation. 3x + 2y = 7 x - y + 3 = 0 _________ 3x + 2y = 7 x + 3  = y _________ 3x + 2y = 7 x = y - 3 _________ 3(y - 3) + 2y = 7 Q13. The answer is p = -2, q = 5 2p + q = 1 9p + 3q + 3 = 0 ________ 2p + q = 1 9p + 3q = -3 ________ Divide the second equation by 3_ 2p + q = 1 (9p + 3q)/3 = -3/3 ________ 2p + q = 1 9p/3 + 3q/3 = -1 ________ 2p + q = 1 3p + q = -1 ________ Solve both equations for q: q = 1 - 2p q = - 3p - 1 ________ Equal the equations: 1 - 2p = -3p - 1 3p - 2p = -1 - 1 p = -2 q = 1 - 2p p = -2 _______ q = 1 - 2 * (-2) q = 1 - (-4) q = 1 + 4 q = 5 Q14. The answer is 4y + 1 = 4 - 5y. Solve both equations for x: x - 4y - 1 = 0 x + 5y - 4 = 0 ______ x - 4y = 1 x + 5y = 4 ______ x = 4y + 1 x = 4 - 5y ______ Equal the equations: 4y + 1 = 4 - 5y Q15. The answer is x = 5, y = -5 Use the x from the second equation and substitute it in the first equation: 3x + 2y - 5 = 0 x = y + 10 ___________ 3(y + 10) + 2y - 5 = 0 3 * y + 3 * 10 + 2y - 5 = 0 3y + 30 + 2y - 5 = 0 3y + 2y + 30 - 5 = 0 5y + 25 = 0 5y = - 25 y = -25/5 y = -5 x = y + 10 y = -5 _______ x = -5 + 10 x = 5

Add answer