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?

Answer 1

8,11

Explanation:

Answer 2

(8, 11)

Explanation:

The 2-point form of the equation of a line is useful for the one where only points are given.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

y = (3 -1)/(4 -3)(x -3) +1

y = 2(x -3) +1

We can equate this to the expression for y in the given equation.

x +3 = 2(x -3) +1

x +3 = 2x -5 . . . . . . eliminate parentheses

8 = x . . . . . . . . . . . . add 5-x

Using the given equation, we can find y:

y = x +3 = 8 +3

y = 11

The solution to the system is (x, y) = (8, 11).