Question

Solve the system of linear equations by substitution. Check your solution.x=17-4yy=x-2

Answer 1

We have the system of equations:

`\begin{gathered} x=17-4y \\ y=x-2 \end{gathered}`

We already have an explicit expression both for x and y so we can use any of the two equations and replace the variable in the other one.

We will substitute y in the first equation, with the information of the second equation, and solve for x:

`\begin{gathered} x=17-4y \\ x=17-4(x-2) \\ x=17-4x+8 \\ x+4x=17+8 \\ 5x=25 \\ x=(25)/(5) \\ x=5 \end{gathered}`

Then, we can use the value of x to calculate y with the second equation:

`y=x-2=5-2=3`

We can check the result by replacing the solution values in the equation and verify that we get a valid result:

`\begin{gathered} x=17-4y \\ 5=17-4\cdot3 \\ 5=17-12 \\ 5=5\longrightarrow\text{True} \end{gathered}`
`\begin{gathered} y=x-2 \\ 3=5-2 \\ 3=3\longrightarrow\text{True} \end{gathered}`

Answer: the solution is x=5 and y=3