Question

Determine whether the given ordered pair is a solution to the system of equations. 6x−2y =36 −3x+3y =12 and (11,15)

Answer 1

Given the system of equations:

• 6x - 2y = 36

,

• -3x + 3y = 12

The solution:

(x, y) ==> (11, 15)

Let's determine whether the given ordered pair is a solution to the system of equations.

Let's solve the system using the addition and elimination method.

Multiply both equations so the coefficients of one variable are opposite.

Multiply equation 2 by 2:

6x - 2y = 36

2(-3x + 3y) = 2(12)

• 6x - 2y = 36

,

• -6x + 6y = 24

Add both equations:

6x - 2y = 36

-6x + 6y = 24

____________

0 + 4y = 60

We now have:

4y = 60

Divide both sides by 4:

`\begin{gathered} (4y)/(4)=(60)/(4) \\ \\ y=15 \end{gathered}`

Plug in 15 for y in either of the equations.

Take the first equation:

`\begin{gathered} 6x-2y=36 \\ \\ 6x-2(15)=36 \\ \\ 6x-30=36 \end{gathered}`

Add 30 to both sides:

`\begin{gathered} 6x-30+30=36+30 \\ \\ 6x=66 \end{gathered}`

Divide both sides by 6:

`\begin{gathered} (6x)/(6)=(66)/(6) \\ \\ x=11 \end{gathered}`

Therefore, the solution is:

x = 11, y = 15

In point form, the solution is: (11, 15)

Therefore, the given ordered pair is a solution to the system of equations.

ANSWER:

Yes, the ordered pair is a solution to the system of equations.