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=(-13-2y)/(7) \end{gathered}`

Now, we can plug this into the II equation.

`\begin{gathered} -3((-13-2y)/(7))-8y=-23 \\ (39)/(7)+(6y)/(7)-8y=-23 \\ (6y)/(7)-8y=-23-(39)/(7) \\ -(50)/(7)y=-(200)/(7) \\ 7*-(50)/(7)y=-(200)/(7)*7 \\ -50y=-200 \\ (-50y)/(-50)=(-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 \\ (7x)/(7)=(-21)/(7) \\ x=-3 \end{gathered}`

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