Question

please explain and walk through problem. Thanks

context: "Solve each system of linear equations by substitution."​

Answer 1

Solving a system by substitution means that you use one equation (in this case, the second) to express one variable in terms of the other (in this case, in the second equation, we express $y$ in terms of $x$.

So, we can substitute this expression for $y$ in the first equation, we have

$3x-2y=9$

But since we know that

$y=2x-7$

We have

$3x-2(2x-7)=9$

We can now solve this equation as usual, since it involves $x$ alone:

$3x-2(2x-7)=9 \iff 3x-4x+14=9 \iff -x = -5 \iff x=5$

And once we know that value for $x$, we can compute $y$:

$y=2x-7=2\cdot 5 - 7 = 3$