Question

Solve by the substitution method.

Answer 1

Answer:

The unique solution to the system is (x,y){(-9,-3)}

Step-by-step explanation:

x - y = -6     equation 1

5x + 6y = -63     equation 2

We will find the value of x from equation 1.

x= y-6

Now put the value of x in equation 2.

5(y-6)+6y = -63

5y-30+6y = -63

Combine the like terms:

5y+6y= -63+30

11y = -33

Divide both sides by 11.

11y/11 = -33/11

y = -3

Now put the value y = -3 in x=y-6

x = y-6

x= -3-6

x= -9

Therefore The unique solution to the system is (x,y){(-9,-3)} ....

Answer 2

Answer: A. The unique solution to the system is $(-9,-3)$

Step-by-step explanation:

You can follow these steps to solve the system of equation by the Substitution Method:

- Solve for "x" from the first equation:

$x - y = -6\\x=-6+y$

- Substitute into the second equation and solve for "y":

$5(-6+y) + 6y = -63\\\\-30+5y+6y=-63\\\\11y=-63+30\\\\y=\frac{-33}{11}\\\\y=-3$

- Sustitute the value of "y" into $x=-6+y$ to find the value of "x":

$x=-6+(-3)\\\\x=-9$

Therefore, the unique solution to the system is:

$(-9,-3)$