Question

Solve the system by substitution type your stepsx=2y-53x-y=5

Answer 1

The solution to the system of equations is

x = 3

y = 4

Step-by-step explanation:

Given the pair of equations:

`\begin{gathered} x=2y-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 3x-y=5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}`

To solve these simultaneously, use the expression for x in equation (1) in equation (2)

`\begin{gathered} 3(2y-5)-y=5 \\ 6y-15-y=5 \\ 6y-y-15=5 \\ 5y-15=5 \\ \\ \text{Add 15 to both sides} \\ 5y-15+15=5+15 \\ 5y=20 \\ \\ \text{Divide both sides by 5} \\ (5y)/(5)=(20)/(5) \\ \\ y=4 \end{gathered}`

Using y = 4 in equation (1)

`\begin{gathered} x=2(4)-5 \\ =8-5 \\ =3 \end{gathered}`

Therefore, x = 3, and y = 4