Question

How do you solve the system of equations `4x - y = 6` and `4x + 5y = - 6`?

Answer 1

`x = 2`
`y = 2`

Explanation:

Eliminate one variable in order to determine the value of the other. Then determine the value of the eliminated variable using the original equations

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Scale one of the equations (or both) such that the coefficient of one of the variables will be equal.

`[1] 4x - y = 6`
`[2] 4x +5y = -6`

In this case, the coefficient of `x` for both equations are already the same. There is no need for us to scale.

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Subtract equations [1] and [2]

<pre>
4x - y = 6
- (4x + 5y = -6)

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0x - 6y = 12

</pre>

`=> 6y = 12`

`=> y = 2`

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Using equation [1], get the value of `x`

`4x - (2) = 6`

`=> 4x -2 = 6`
`=> 4x = 8`
`=> x = 2`