Question

Solve the system by substitution:$\left\{\begin{array}{l}-2x+y=-11\\ x+3y=9\end{array}\right.$

Short answer

Solution of the system of equations is$(6,1)$.

Step-by-step solution

Step 1. Given Information.

System of equations is$\left\{\begin{array}{l}-2x+y=-11\\ x+3y=9\end{array}\right.$

Step 2. Solve one of the equations for either variable.

We'll solve for the first equation for y.

$-2x+y=-11$

$y=2x-11$

Step 3. Substitute the expression from Step 2 into the other equation.

We replace $y$in the second equation with the expression $2x-11$.

$x+3y=9$

$x+3(2x-11)=9$

Step 4. Solve the resulting equation.

Now we have an equation with just one variable.

$x+3(2x-11)=9$

$x+6x-33=9$

$7x=42$

$x=6$

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

We'll use the first equation and replace $x$with 6.

$-2x+y=-11$

$-2\left(6\right)+y=-11$

$-12+y=-11$

$y=1$

Step 6. Write the solution as an ordered pair.

The ordered pair is $(x,y).$

$(6,1)$

Step 7. Check that the ordered pair is a solution to both original equations.

Substitute $x,y=6,1$into both equations and make sure they are both true.

$-2x+y=-11$

$-2\left(6\right)+1=-11$

$-11=-11$

And, $x+3y=9$

$6+3\left(1\right)=9$

$9=9$

Both equations are True.

$(6,1)$is the solution to the system.