Question

Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11

Answer 1

Explanation:

We have the following simultaneous system of equations:

• -7x - 2y = -13 and x - 2y = 11.

=> 7x + 2y = 13 and x - 2y = 11.

Adding them, we have 8x = 24, so x = 3.

Consequently, y = (x - 11)/2 = -4.

Answer 2

The given steps in the correct order are:

• 
  `x-2y=11 \rightarrow x=2y+11`
• 
  `-7(2y+11)-2y=-13`
• 
  `-14y-77-2y=-13`
• 
  `-16y-77=-13`
• 
  `-16y=64`
• 
  `y=-4`
• 
  `x=2(-4)+11 \rightarrow x=3`
• 
  `(3, -4)`

Explanation:

Given system of equations:

`\begin{cases}-7x-2y=-13\\x-2y=11\end{cases}`

To solve the system of equations by the method of substitution, begin by adding 2y to both sides of the second equation to isolate x:

`x-2y=11 \rightarrow x=2y+11`

Now, substitute the expression for x into the first equation:

`-7(2y+11)-2y=-13`

Next, distribute the -7 on the left side:

`-14y-77-2y=-13`

Combine like terms:

`-16y-77=-13`

Add 77 to both sides of the equation:

`-16y=64`

Divide both sides of the equation by -16:

`y=-4`

Substitute the found value of y into the expression for x:

`x=2(-4)+11 \rightarrow x=3`

Therefore, the solution of the system of equations is:

`(3, -4)`