Question

PLEASE HELP!

Solve the system by graphing

Y= 1/2x+3/2
Y=2x-3
1. Graph each line.
2. Solve the system
3. Explain what the solution of system of linear equations represent.

Answer 1

`\bf \begin{cases} y=\cfrac{1}{2}x+\cfrac{3}{2}\\\\ \boxed{y}=2x-3 \end{cases}~\hspace{5em}\stackrel{\textit{using substitution}}{\boxed{2x-3}=\cfrac{1}{2}x+\cfrac{3}{2}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(2x-3)=2\left( \cfrac{1}{2}x+\cfrac{3}{2} \right)}\implies 4x-6=x+3\implies 3x=9`

`\bf x=\cfrac{9}{3}\implies \blacktriangleright x=3 \blacktriangleleft \\\\\\ \stackrel{\textit{using the found \underline{x} in the 2nd equation}}{y=2(3)-3\implies y=6-3}\implies \blacktriangleright y=3 \blacktriangleleft`

what does the solution mean? check the picture below.