Question

2x+2y=6 3x-y=5 equivalent equation

Answer 1

x = 2, y = 1

Explanation:

Given:

`\begin{bmatrix}2x+2y=6\\ 3x-y=5\end{bmatrix}`

Solve:

`\mathrm{Isolate\;x\;for\;2x+2y=6:x=3-y}`

`\mathrm{Substitute\:}`

`\begin{bmatrix}3\left(3-y\right)-y=5\end{bmatrix}`

`\mathrm{Simplfy}`

`\begin{bmatrix}9-4y=5\end{bmatrix}`

`\mathrm{Isolate\;y\;for\;9-4y=5:y=1}`

`\mathrm{For\:}x=3-y\;\mathrm{Substitute\:}y=1`

`x=3-1`

`\mathrm{Simplify}`

`x=2`

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

`x=2,\:y=1`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check Answer:

Since
`x =2 , y =1`

`2(2)+2(1)`

`4 + 2`

`= 6`

True

`3(2) - (1)`

`6 -1`

`5`

True

Hence,
`x = 2, y = 1`

~Lenvy~