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

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 $(2,2)$

Answer 2

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