Please Help if You Want PRE ALGEBRA Two lines, M and N, are represented by the following equations:

Line M: y = x + 3

Line N: y = −2x + 6

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

(1, 4), because the point does not lie on any axis

(1, 4), because one of the lines passes through this point

(1, 4), because both lines pass through this point

(1, 4), because the point lies between the two axes

Third answer shown

Step-by-step explanation:

Since each equation has a right side equal to the same thing, y, those right sides must be equal to each other.

                                                    x + 3 = -2x + 6

Add 2x to both sides.                2x          2x

                                                   3x + 3 =  0 + 6

                                                   3x + 3 = 6

Subtract 3 on both sides.                -3     -3

                                                      3x    =    3

Divide both sides by 3.                   x = 1

Now, let's see what y must be if x equals 1.

Line M:  y = x + 3 -->  y = 1 + 3 --> y = 4

Line N: y = -2x +6 --> y = -2(1) +6 --> y = -2 + 6 --> y = 4, confirmed

So the ordered pair (x, y) that satisfies both equations is (1, 4)

*** This means that if you graphed both lines on an xy-coordinate plane, the point (1,4) would be the point where the two lines intersect.

That is the third answer shown.

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step-by-step explanation: