Question

Is (-7, -3) a solution to this system of equations?

x = -7
y = -x - 10

Yes or no

Answer 1

Answer: Yes

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Step-by-step explanation:

The point (-7,-3) means x = -7 and x = -3

Right off the bat, the first equation x = -7 is proven true based on the first coordinate.

Let's now plug the coordinates into the second equation.

y = -x-10

-3 = -(-7)-10

-3 = 7-10

-3 = -3

Which is a true statement.

Both equations are true when (x,y) = (-7,-3)

This is why it is a solution to the system. It turns out it's the only solution to this system. This system is consistent and independent.

You can use a graphing tool like Desmos to plot the two equations, and you should see them crossing at the point (-7,-3)

Answer 2

The answer is yes

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

x = -7

y = -x - 10

For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.

First, I will substitute the first equation, for x, into the first equation:

x = -7

y = -x - 10

y = -(-7) - 10 <== multiplying two negatives, makes a positive

y = 7 - 10

y = - 3 <== the value of y

Now, we find the value of x by substituting - 3 for y:

y = -x - 10

- 3 = -x - 10

+10 +10

7 = -x <== you can't have a negative variable

/-1 /-1

-7 = x <== the value of x

(x, y) ==> (-7, -3)

Therefore, yes (-7,-3) is a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!