Question

What is the solution to the system of equations below?

y = negative 6 x minus 10 and y = negative one-half x minus 21
(2, –22)
(2, 48)
(–2, 2)
(–2, –20)

Answer 1

We have been given a system of equations. $y=-6x-10$ and $y=-\frac{1}{2}x-21$. We are asked to find the solution of our given system of equations.

To find the solution of our given system of equations, we will equate both equations as:

$-6x-10=-\frac{1}{2}x-21$

$-6x-10+10=-\frac{1}{2}x-21+10$

$-6x=-\frac{1}{2}x-11$

$-6x+\frac{1}{2}x=-\frac{1}{2}x+\frac{1}{2}x-11$

$-\frac{12}{2}x+\frac{1}{2}x=-11$

$-\frac{11}{2}x=-11$

$\frac{-2}{11}\cdot -\frac{11}{2}x=-11\cdot \frac{-2}{11}$

$x=2$

Upon substituting $x=2$ in equation $y=-6x-10$, we will get:

$y=-6x-10\Rightarrow -6(2)-10=-12-10=-22$

Therefore, the solution of our given system of equations would be $(2,-22)$ and option A is the correct choice.

Answer 2

By solving the system of equations by substitution, we will see that the solution is (2, -22)

So the system of equations is:

y = -6x - 10

y = -(1/2)x - 21

To solve it, we can replace "y" in the second equation by the equivalent expression in the first equation, this gives:

-6x - 10 = y  =  -(1/2)x - 21

-6x - 10 = -(1/2)x - 21

Now we can solve this for x.

-6x + (1/2)x = -21 + 10

(1/2 - 6)*x = -11

(-11/2)*x = -11

x = -11*(-2/11) = 2

x = 2

To get the y-value we just need to evaluate one of the lines in x = 2.

y = -6*(2) - 10 = -12 - 10 = -22

Then the solution of the system is (2, -22)

If you want to learn more about systems of equations, you can read:

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