Question

8. Solve the following system of equations using substitution, elimination, or

elimination by multiplication.

2x + 3y = 14
3x – 4y = 4

A. (2,4)
B. (4,2)
C. (-4, 22/3)
D. (3,5)

Answer 1

B

Explanation:

given the system of equations

2x + 3y = 14 → (1)

3x - 4y = 4 → (2)

multiplying (1) by 4 and (2) by 3 and adding the result will eliminate y

8x + 12y = 56 → (3)

9x - 12y = 12 → (4)

add (3) and (4) term by term to eliminate y

(8x + 9x) + (12y - 12y) = 56 + 12

17x + 0 = 68

17x = 68 ( divide both sides by 17 )

x = 4

substitute x = 4 into either of the 2 original equations and solve for y

substituting into (1)

2(4) + 3y = 14

8 + 3y = 14 ( subtract 8 from both sides )

3y = 6 ( divide both sides by 3 )

y = 2

solution is (4, 2 )