Question

A system of equations is graphed on the coordinate plane. y=−6x−3y=−x+2 What is the solution to the system of equations? Enter the coordinates of the solution in the boxes

Answer 1

Given system : y=−6x−3 and y=−x+2.

For first equation y=−6x−3 , slope rise/run = -6/1 and y-intercept -3.

Plotting y-intercept (0,-3) first and then find other coordinate using rise/run = -6/1.

Joining the points and draw a line.

For first equation y=−x+2 , slope rise/run = -1/1 and y-intercept 2.

Plotting y-intercept (0,2) first and then find other coordinate using rise/run = -1/1.

Joining the points and draw a line.

Lines cross at (-1,3) point.

Therefore, solution is (-1,3).

Answer 2

If you equate both, the y is eliminated:

-6x-3 = -x+2

Simplify this to find x:

-5x = 5
x = -1

Fill in x=-1 in either equation:

y = --1 + 2 = 3

So (-1,3) is the solution, it is where the lines intercept.