Question

X=3y+12x+4y=12Solve each system by Substitution

Answer 1

`\text{ The solution of the system is }(4,1)`

Explanation:

The substitution method consists in isolating one of the variables and plugging it into the other equation. Given the following system of equations, solve for substitution:

`\begin{gathered} x=3y+1\text{ }(1) \\ 2x+4y=12\text{ }(2) \end{gathered}`

Since ''x'' is already isolated in (1), plug it into equation (2):

`\begin{gathered} 2(3y+1)+4y=12 \\ \text{ Using distributive property:} \\ 6y+2+4y=12 \\ 10y+2=12 \end{gathered}`

Solve for y.

`\begin{gathered} 10y=10 \\ y=(10)/(10) \\ y=1 \end{gathered}`

Now, knowing the y-value for the solution of the system. Substitute y=1 into equation (1):

`\begin{gathered} x=3y+1 \\ x=3(1)+1 \\ x=4 \end{gathered}`
`\text{ The solution of the system is }(4,1)`