Question

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.

2x – 7y = 4

3x + y = –17

Answer 1

Equation 1:
`2x-7y=4`
Equation 2:
`3x+y=-17`

Rearranging equation 2 to make 'y' the subject


`y = -17 - 3x` ⇒ Call this Equation 3

Substituting Equation 3 into Equation 1

`2x-7(-17-3x)=4`

`2x+119+21x=4`

`23x+119=4`

`23x=4-119`

`23x=-115`

`x=-5`

Then substitute x = -5 into either Equation 1 or Equation 2 to solve for 'y'


`2x-7y=4`

`2(-5)-7y=4`

`-10-7y=4`

`-7y=4+10`

`-7y=14`

`y=-2`

Note: the original question did not attach the option for the equation after substitution so you might want to follow the working out here carefully and match it with the options given.