Question

Solve each system of equations by using either substitution or elimination.

$\begin{array}{l}3.y=x+5\\ x+y=9\end{array}$

Short answer

The solution of the system of equations is $\left(2 , 7\right)$.

Step-by-step solution

Step-1 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-2 – Substitute the expression

Since, the first equation is already in expressed for y in terms of x so substitute $y=x+5$in the equation$x+y=9$ and solve.

$\begin{array}{l}x+y=9\\ x+x+5=9\\ 2x=4\\ x=2\end{array}$

Thus, the value of x is $2$.

Step-3 – Substitute the value of variable

To find the value of y, substitute $x=2$in the equation $x+y=9$and then solve as shown.

$\begin{array}{l}x+y=9\\ 2+y=9\\ y=7\end{array}$

Thus, the value of y is $7$.

Hence, the solution of the provided system of equations is $\left(2 , 7\right)$.