\(4x + y + 3z = 34\)
\(4x + 3z = 21\)

What is the value of \(y\)?

This is a system of equations with 3 variables and 2 equations. We need to eliminate \(z\), if we want to solve this system of equations. We can then solve for \(x\) and \(y\). But we see that we can eliminate the variables \(x\) and \(z\) by subtracting one equation from another. We will then be left with y, whose value we want.

We rearrange the equations and subtract

\(4x + 3z + 1y= 34\)
\(4x + 3z + 0y= 21\)
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\(y = 13\)
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We automatically obtain \(y = 13\)