Question

Solve by the substitution method.

x - y = -6
5x + 6y = -63

What is the solution of the​ system? Select the correct choice below and fill in the answer box within your choice.

A.The unique solution to the system is ___ ​(Type an ordered​ pair.)
B.There are an infinite number of solutions.
C.There is no solution.

Answer 1

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

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=(-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)`

Answer 2

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

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)} ....