Question

A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3). On a coordinate plane, a line goes through (0, 3) and (2, 5). What is the solution to the system of equations? (–1, 2) (1, 3) (8, 11) (9, 12)

Answer 1

C: (8,11)

Explanation:

Answer 2

The solution to the system of equations is (8,11)

Explanation:

A system of linear equations includes the line that is created by the equation y = x+ 3

The line through the points (3, 1) and (4, 3)

`(x_1,y_1)=(3,1)\\(x_2,y_2)=(4,3)`

Equation of line =
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Equation of line =
`y-1=(3-1)/(4-3)(x-3)`

Equation of line =y-1=2x-6

Equation of line =y=2x-5

On a coordinate plane, a line goes through (0, 3) and (2, 5).

`(x_1,y_1)=(0,3)\\(x_2,y_2)=(2,5)`

Equation of line =
`y-3=(5-3)/(2-0)(x-0)`

Equation of line =y=2x+3

Plot all lines on graph

y = x+ 3 ---- Blue line

y=2x-5 --- Green line

y=2x+3 ---- Purple line

Refer the attached figure :

Hence the solution to the system of equations is (8,11)