Question

In the following exercises, solve each system of equations. Use either substitution or elimination.

$\left\{\begin{array}{l}x+4y=6\\ -2x+y=-3\end{array}\right.$

Short answer

The solution for the system of the equation $\left\{\begin{array}{l}x+4y=6\\ -2x+y=-3\end{array}\right.$ is $(2,1)$

Step-by-step solution

Step 1. Given

The system of equations $\left\{\begin{array}{l}x+4y=6\\ -2x+y=-3\end{array}\right.$

To find the solution of the system of equations.

Step 2. Solve the equations

Consider the system of equations:

$x+4y=6$

$-2x+y=-3$

Solve the first equation for $x$,

$x=6-4y$

Step 3. Solve for y

Substitute $x=6-4y$in the second equation,

$-2(6-4y)+y=-3$

$-12+8y+y=-3$

$9y=9$

Divide both sides of the equation by $9$,

$y=1$

Step 4. Solve for x

Substitute $y=1$in the first equation,

$x+4y=6$

$x+4\left(1\right)=6$

$x=6-4$

$x=2$

The solution of the equation is $(2,1)$

Step 5. Check the solution

Substitute $(2,1)$in both the equations,

$x+4y=6$

$2+4\left(1\right)=6$

$6=6$is true.

Then $-2x+y=-3$

$-2\left(2\right)+1=-3$

$-3=-3$is true.

Hence the solution has been checked.