Question

Solve the system by substitution:$\left\{\begin{array}{l}2x+y=-1\\ 4x+3y=3\end{array}\right.$

Short answer

The solution of the system of equations is$(-3,5)$.

Step-by-step solution

Step 1. Given Information. 

The system of equations is $\left\{\begin{array}{l}2x+y=-1\\ 4x+3y=3\end{array}\right.$.

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

We'll solve for the first equation for y,

$2x+y=-1$

$y=-2x-1$

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

We replace y in the second equation with the expression $-2x-1$.

$4x+3y=3$

$4x+3(-2x-1)=3$

Step 4. Solve the resulting equation. 

Now we have an equation with just one variable.

$4x+3(-2x-1)=3$

$4x-6x-3=3$

$-2x=6$

$x=-3$

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 $-3$

$2x+y=-1$

$2(-3)+y=-1$

$-6+y=-1$

$y=5$

Step 6. Write the solution as an ordered pair. 

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

$(-3,5)$

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

Substitute $x,y=-3,5$into both equations and make sure they are both true.

$2x+y=-1$

$2(-3)+5=-1$

$-1=-1$

And, $4x+3y=3$

$4(-3)+3\left(5\right)=3$

$-12+15=3$

$3=3$

Both equations are True.

The point$(-3,5)$is the solution to the system.