Question

This graph represents the system of equations below: What is the solution (the values of x and y that are true for both equations)? Fill in the coordinates of the ordered pair:

Answer 1

$(\frac{22}{5},\frac{11}{5})$

Explanation

$\begin{gathered} 3x+4y=22 \\ 2x+6y=22 \end{gathered}$

Step 1

isolate x in both equations

$\begin{gathered} 3x+4y=22 \\ 3x=22-4y \\ x=\frac{22}{3}-\frac{4}{3}y \\ \text{and} \\ 2x+6y=22 \\ 2x=22-6y \\ x=\frac{22}{2}-\frac{6}{2}y \\ x=11-3y \end{gathered}$

Step 2

x= x, then

$\begin{gathered} \frac{22}{3}-\frac{4}{3}y=11-3y \\ -\frac{4}{3}y+3y=11-\frac{22}{3} \\ y(-\frac{4}{3}+3)=\frac{11}{3} \\ y(\frac{5}{3})=\frac{11}{3} \\ y=\frac{11}{3}\cdot\frac{3}{5} \\ y=\frac{11}{5} \end{gathered}$

Step 3

finally, replace the y-value to find x

$\begin{gathered} x=11-3y \\ x=11-3\cdot\frac{11}{5} \\ x=11-\frac{33}{5} \\ x=\frac{22}{5} \end{gathered}$

I hope this helps you