Question

Choose the system of equations that matches the following graph:

A. 3x + 7y = 7
5x + 7y = −63

B. 3x + 7y = 7
5x − 7y = −63

C. 3x − 7y = 7
5x + 7y = −63

D. 3x − 7y = 7
5x − 7y = −63

Answer 1

we see that (-7,4) is the intersection
therefor x=-7 and y=4 must be true for those 2 equations

another way
the slopes must be negative then positive
not A nor D
test x=-7 and y=4
B works

B is answer

Answer 2

Option B.

3x + 7y = 7

5x − 7y = −63

Explanation:

Given : Graph of two equations.

To find : Choose the system of equations that matches the following graph?

Solution :

First we examine the graph in which both the lines intersect at one point i.e, (-7,4)

So, from the following equation when both the equation satisfying the point is the required equations.

A.

3x + 7y = 7 5x + 7y = −63

3(-7)+7(4) = 7 5(-7) + 7(4) = −63

-21 + 28 = 7 -35+28 = −63

7 = 7 -7 ≠ −63

This equation is not true.

B.

3x + 7y = 7 5x - 7y = -63

3(-7)+7(4) = 7 5(-7) - 7(4) = -63

-21 + 28 = 7 -35-28 = -63

7 = 7 -63= -63

This equation is true.

C.

3x - 7y = 7 5x + 7y = -63

3(-7)-7(4) = 7 5(-7) + 7(4) = -63

-21 - 28 = 7 -35+28 = -63

-49 ≠ 7 -7 ≠ -63

This equation is not true.

D.

3x - 7y = 7 5x - 7y = -63

3(-7)-7(4) = 7 5(-7) - 7(4) = -63

-21 - 28 = 7 -35-28 = -63

-49 ≠ 7 -63 = -63

This equation is not true.

Only equation B satisfy the intersection point.

Therefore,Option B is correct.