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

Answer:

C: (8,11)

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step 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 =$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Equation of line =$y-1=\frac{3-1}{4-3}(x-3)$

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 =$y-3=\frac{5-3}{2-0}(x-0)$

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)