Solve the following system of linear equations. `4x+4y+z=24` `12y-z=24` `9x-4z=36`
Solve the following system of linear equations.
`4x+4y+z=24`
`12y-z=24`
`9x-4z=36`
Solution:
Notice that in this system, equation 2 and equation 3 are each missing a variable and are each missing different variables. There are many ways to approach this problem. The way I approach these is to compare the first equation to either the second or third equation. I will choose to compare the first equation and the second equation.
`4x+4y+z=24`
12y-z=24`
Notice that the first equation has a +z and the second equation has a -z. You might be tempted to eliminate the z's but if you do that, the resulting equation will have an x and a y in it. The problem with that is that the third equation has an x and a z in it. So I would not be able to pair those two together. Ideally, since the third equation (the one I am not using right now), has only an x and a z in it, we should try to eliminate y. The best way to do that is to multiply the first equation, `4x+4y+z=24`, through by -3. Do that and enter your new equation below.
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