Question

determine whether the given ordered pair is a solution to the system of equations. 5. $y = -6x$ $y = \frac{1}{2}x + 7$ $(-2, 6)$ 6. $x + 5y = 8$ $4x - 5y = 7$ $(3, 1)$ 7. $y = x - 9$ $x + y = -1$ $(4, -5)$

Explanation:

Problem 5: Ordered pair (-2,8)

Step1: Substitute into first equation

Substitute $x=-2$, $y=8$ into $y=-4x$:
$8 = -4\times(-2)$
$8=8$ (True)

Step2: Substitute into second equation

Substitute $x=-2$, $y=8$ into $y=\frac{1}{2}x+7$:
$8 = \frac{1}{2}\times(-2)+7$
$8 = -1+7$
$8=6$ (False)

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Problem 6: Ordered pair (3,1)

Step1: Substitute into first equation

Substitute $x=3$, $y=1$ into $x+5y=8$:
$3 + 5\times1 = 8$
$3+5=8$
$8=8$ (True)

Step2: Substitute into second equation

Substitute $x=3$, $y=1$ into $4x-5y=7$:
$4\times3 - 5\times1 = 7$
$12-5=7$
$7=7$ (True)

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Problem 7: Ordered pair (4,-5)

Step1: Substitute into first equation

Substitute $x=4$, $y=-5$ into $y=x-9$:
$-5 = 4-9$
$-5=-5$ (True)

Step2: Substitute into second equation

Substitute $x=4$, $y=-5$ into $x+y=-1$:
$4 + (-5) = -1$
$-1=-1$ (True)

Answer:

1. The ordered pair $(-2,8)$ is not a solution to the system.
2. The ordered pair $(3,1)$ is a solution to the system.
3. The ordered pair $(4,-5)$ is a solution to the system.