Question

For each ordered pair, determine whether it is a solution to the system of equations.

=−7x4y8=+−2x3y7

Is it a solution?
x, y

−−9, 6


7, 7


−0, 2


4, 5

Answer 1

The system of equations is:

-7x + 4y = 8

-2x + 3y = 7

Let's substitute the values of x and y from each ordered pair and see if the equations hold true:

Ordered pair: (-9, 6)

Substituting x = -9 and y = 6 into the equations:

-7(-9) + 4(6) = 63 + 24 = 87 ≠ 8 (Not a solution)

-2(-9) + 3(6) = 18 + 18 = 36 ≠ 7 (Not a solution)

Ordered pair: (7, 7)

Substituting x = 7 and y = 7 into the equations:

-7(7) + 4(7) = -49 + 28 = -21 ≠ 8 (Not a solution)

-2(7) + 3(7) = -14 + 21 = 7 (A solution)

Ordered pair: (0, 2)

Substituting x = 0 and y = 2 into the equations:

-7(0) + 4(2) = 0 + 8 = 8 (A solution)

-2(0) + 3(2) = 0 + 6 = 6 ≠ 7 (Not a solution)

Ordered pair: (4, 5)

Substituting x = 4 and y = 5 into the equations:

-7(4) + 4(5) = -28 + 20 = -8 ≠ 8 (Not a solution)

-2(4) + 3(5) = -8 + 15 = 7 (A solution)

To summarize:

The ordered pair (-9, 6) is not a solution to the system of equations.

The ordered pair (7, 7) is not a solution to the system of equations.

The ordered pair (0, 2) is not a solution to the system of equations.

The ordered pair (4, 5) is a solution to the system of equations.

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