Question

Solve the system of equations. (6 points)

​2x - 3y = 21 and -6x + 2y = 7
Part I: Would substitution or elimination be the more efficient strategy to simplify this system of equations? Explain your answer. (1 point)
Part II: Explain the steps you would take to solve the system by eliminating the x-terms. (2 points)
Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)
Solve the system of equations. (6 points)

​2x - 3y = 21 and -6x + 2y = 7
Part I: Would substitution or elimination be the more efficient strategy to simplify this system of equations? Explain your answer. (1 point)
Part II: Explain the steps you would take to solve the system by eliminating the x-terms. (2 points)
Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)

Answer 1

Part I
Elimination is more efficient because the x-coefficients 2 and −6 are already multiples. You can eliminate x by scaling one equation (no messy fractions), so you avoid extra substitution steps.

Part II
1. Multiply the first equation by 3 to make its x-coefficient 6: 3(2x − 3y) = 3(21) → 6x − 9y = 63.
2. Add this to the second equation (−6x + 2y = 7). The 6x and −6x cancel, leaving an equation in y only.
3. Solve that equation for y, then substitute y into either original equation and solve for x.

Part III (solve the system)
Multiply the first equation by 3:
6x − 9y = 63
Add the second equation −6x + 2y = 7:
(6x − 9y) + (−6x + 2y) = 63 + 7
−7y = 70
y = −10

Substitute y = −10 into 2x − 3y = 21:
2x − 3(−10) = 21
2x + 30 = 21
2x = −9
x = −9/2

Solution as an ordered pair: (−9/2, −10).