Question

Solve the system of equations.
2y+7x=−5
5y−7x=12
​

Answer 1

We can solve this by substitution method.

Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.

`5y-7x=12`

`5y-7x-12=0`

`5y-12=7x`

Therefore,
`7x=5y-12`

Now replace the 7x in the first equation with 5y - 12:

`2y+7x=-5` (substitute in 7x = 5y - 12)

`2y+(5y-12)=-5`

`7y-12=-5`

`7y=7`

`y=1`

Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12

`7x=5y-12` (substitute in y = 1)

`7x=5(1) -12`

`5x=5-12`

`7x=-7`

`x=-1`

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Answer:

`y=1\\x=-1`