Solve the following system of linear equations. `6x-y+3z=-9` `5x+5y-5z=20` `3x-y+4z=-5`
Solve the following system of linear equations.
`6x-y+3z=-9`
`5x+5y-5z=20`
`3x-y+4z=-5`
Solution:
Since the "easiest" variable to eliminate is the `y,` let's eliminate that variable. Our goal is to eliminate the `y` twice.
We can only use two equations at a time. Let's pair the first equation and the second equation together and eliminate y.
`6x-y+3z=-9`
`5x+5y-5z=20`
Multiply every term in the equation `6x-y+3z=-9` by the number that causes the `y's` "cancel". Submit the new equation below.
Try again. Since the `y` in the equation `5x+5y-5z=20` has a `+5` as the coefficent, we want the `y` in the equation `6x-y+3z=-9` to be a `-5`.
Currently, the `y` is a `-1`. What can we multiply `-1` by to be a `-5`? Multiply every term in this equation by that number.
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