Question

A system of equations is graphed on a coordinate plane. Which coordinates are the best estimate of the solution to the system of equations? (2, 3) (1, 2) (2, 2) (2, 4)

Answer 1

a solution for a system of equations graph wise, is where they equations intersect or meet.  check the picture below.

Answer 2

we have

`5x-y=9` ---> equation A

`2x+6y=13` ---> equation B

we know that

The solution of the system of linear equations is the intersection point both graphs

Multiply the equation A by
`6` both sides

`6(5x-y)=6*9`

`30x-6y=54` ------> equation C

Adds equation B and equation C

`2x+6y=13\\30x-6y=54\\------- \\2x+30x=13+54 \\32x=67 \\x=67/32 \\x=2.09`

Find the value of y

substitute in the equation A

`5*2.09-y=9`

`y=10.47-9=1.47`

therefore

the answer is

The best estimate of the solution to the system of equations is the point
`(2,2)`