Question

A system of equations is graphed on the coordinate plane. y = -6x - 3, y = -x + 2, what is the solution of equations?

Answer 1

(x, y ) → (- 1, 3 )

The solution to the system of equations is the point of intersection of the 2 lines

From the graph, that is (x, y ) → ( - 1, 3 )

We can confirm by solving algebraically

Since both equations express y in terms of x we can equate the right sides

- x + 2 = - 6x - 3 ( add 6x to both sides )

5x + 2 = - 3 ( subtract 2 from both sides )

5x = - 5 ( divide both sides by 5 )

x = - 1

substitute x = - 1 into either of the 2 equations for y-coordinate

y = - x + 2 = 1 + 2 = 3

solution is (x, y ) → (- 1, 3 )