Question

Here is a system of linear equations

2x+3y=14
4x-3y=10

Which would be more helpful for solving the system: adding the two equations or subtracting one from the other?

Answer 1

adding the 2 equations

Explanation:

2x + 3y = 14 → (1)

4x - 3y = 10 → (2)

since the coefficients of the y- terms are opposites then adding will eliminate y

add (1) and (2) term by term

6x + 0 = 24

6x = 24 ( divide both sides by 6 )

x = 4

substitute x = 4 into either of the 2 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 )