Question

How do you solve `3x – 2y = 26` and `-7x + 3y = -49` using substitution?

Answer 1

`x = 4`
`y =-7`

Explanation:

Solve by simultaneous equations:

`3x - 2y = 26`
`-7x+3y = -49`

Rearrange `3x - 2y = 26` to make `x` the subject of the equation:

`3x = 26 + 2y`
`x = (26 + 2y) / 3`

Substitute the value of `x` into `-7x+3y = -49`:
`-7*((26 + 2y) / 3) + 3y = -49`
`-7*(26/3 + (2y)/3) + 3y = -49`

Multiply out the brackets:
`-182/3 + -(14y)/3 + 3y = -49`

Rearrange and place like terms together:
`-(14y)/3 + 3y = -49 + 182/3`

Simplify and solve for y:

`-(5y)/3 = 35/3`
`-5y = 35/3 *3`
`-5y = 35`
`y = 35 / -5`
`y = -7`

Use value of y to subsitute into any of the two original equations and solve for x:

`3x - 2y = 26`
`3x - 2*(-7) = 26`
`3x + 14 = 26`
`3x = 26 - 14`
`3x = 12`
`x = 12/3`
`x = 4`