Question

Solve each system by substitution. Tell whether the system has one solution ,infinitely many solutions,or no solution

Answer 1

$x=-3,y=4$

22) In order to make use of the Substitution Method, we need to rewrite one of those equations

7x+2y=-13

-3x-8y=23

22.1) So let's rewrite the first equation:

$\begin{gathered} 7x+2y=-13 \\ 7x=-13-2y \\ x=\frac{-13-2y}{7} \end{gathered}$

Now, we can plug this into the II equation.

$\begin{gathered} -3(\frac{-13-2y}{7})-8y=-23 \\ \frac{39}{7}+\frac{6y}{7}-8y=-23 \\ \frac{6y}{7}-8y=-23-\frac{39}{7} \\ -\frac{50}{7}y=-\frac{200}{7} \\ 7\times-\frac{50}{7}y=-\frac{200}{7}\times7 \\ -50y=-200 \\ \frac{-50y}{-50}=\frac{-200}{-50} \\ y=4 \end{gathered}$

With this step, we could find the quantity of y. Let's plug into any equation, usually the simplest one (for convenience)

22.2)

$\begin{gathered} 7x+2y=-13 \\ 7x+2(4)=-13 \\ 7x+8=-13 \\ 7x+8-8=-13-8 \\ 7x=-21 \\ \frac{7x}{7}=\frac{-21}{7} \\ x=-3 \end{gathered}$

And then the answer is x=-3, y=4