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

`((22)/(5),(11)/(5))`

Step-by-step 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=(22)/(3)-(4)/(3)y \\ \text{and} \\ 2x+6y=22 \\ 2x=22-6y \\ x=(22)/(2)-(6)/(2)y \\ x=11-3y \end{gathered}`

Step 2

x= x, then

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

Step 3

finally, replace the y-value to find x

`\begin{gathered} x=11-3y \\ x=11-3\cdot(11)/(5) \\ x=11-(33)/(5) \\ x=(22)/(5) \end{gathered}`

I hope this helps you