Question

Solve the system of equations by substitution.

3x - 4y = 13
5x + 4y = 11
The solution of the system is x = and y=
(Type integers or simplified fractions.)

Answer 1

You can see how I get the answer in the picture below. Hope it can help you.

Answer 2

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=3,\:y=-1`

Explanation:

`3x - 4y = 13`

`5x + 4y = 11`

isolate x for 3x-4y=13

`\mathrm{Subsititute\:}x=(13+4y)/(3)`

`\begin{bmatrix}5\cdot (13+4y)/(3)+4y=11\end{bmatrix}`

`(65+32y)/(3)=11`

now isolate y for
`(65+32y)/(3)=11`

`(65+32y)/(3)=11`

`65+32y=33`

`32y=-32`

Divide both sides by 32

`(32y)/(32)=(-32)/(32)`

`y=-1`

`\mathrm{For\:}x=(13+4y)/(3)`

`\mathrm{Subsititute\:}y=-1`

`x=(13+4\left(-1\right))/(3)`

`=(13-4\cdot \:1)/(3)`

`=(9)/(3)`

`\mathrm{Divide\:the\:numbers:}\:(9)/(3)=3`

`=3`

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=3,\:y=-1`