Question

X = 2y - 6y = 3x - 7substitution to solve systems of equations

Answer 1

The solution to the pair of equations are

x = 4

y = 8

Step-by-step explanation:

Given the pair of equations:

`\begin{gathered} x=2y-6\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ y=3x-7\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \end{gathered}`

Using substitution

Substitute equation (2) into (1)

`\begin{gathered} x=2(3x-7)-6 \\ =6x-14-6 \\ x=6x-20 \end{gathered}`

Subtract x from both sides

`\begin{gathered} x-x=6x-20-x \\ 0=5x-20 \end{gathered}`

Add 20 to both sides

`\begin{gathered} 0+20=5x-20+20 \\ 20=5x \end{gathered}`

Divide both sides by 5

`\begin{gathered} (20)/(5)=(5x)/(5) \\ \\ 4=x \end{gathered}`

Therefore, x = 5

Substitute x = 5 in equation (2)

`\begin{gathered} y=3(5)-7 \\ =15-7 \\ =8 \end{gathered}`

Therefore, y = 8