Question

Two lines, C and D, are represented by the following equations:

Line C: y = x + 5
Line D: y = −2x − 1

Which of the following options shows the solution to the system of equations and explains why?

(−2, 3), because the point does not lie on any axis
(−2, 3), because both lines pass through this point
(−2, 3), because one of the lines passes through this point
(−2, 3), because the point lies between the two axes

Answer 1

(−2, 3), because both lines pass through this point

Explanation:

Line C: y = x + 5

Line D: y = −2x − 1

Substitute x+5 for y in second equation

x + 5 = -2x -1

add 2x on both sides

3x + 5= -1

subtract 5 from both sides'

3x = -6

divide both sides by 3

x= -2

Now plug in -2 for x in y=x+5

y=-2+5= 3

so x= -2, y= 3

both lines satisfies the point (-2,3) (intersection point)

(−2, 3), because both lines pass through this point

Answer 2

(−2, 3), because both lines pass through this point

Explanation:

The meaning of "solution to the system of equations" is that both lines intersect at the solution point. That is, they both pass through that point.