Decide whether elimination or substitution seems easier here. Look at the coefficients of $x$ and $y$ in both equations and think about which variable you could eliminate more quickly.

The $y$-coefficients are $1$ and $-3$. What could you multiply one of the equations by so that the $y$-terms become opposites and cancel when you add the equations?

After you find one variable, be sure to plug it back into one of the original equations to solve for the other variable, and then check both equations.

In Desmos, type 4x + y = 22 on one line and 2x - 3y = -10 on another line so both lines are graphed on the same coordinate plane.

Zoom or pan the graph until you see where the two lines cross. Click on the intersection point; Desmos will display its coordinates. Those coordinates give the ordered pair that satisfies both equations.

We are given two equations in $x$ and $y$:

We need a single ordered pair $(x,y)$ that makes both equations true at the same time, not just one of them.

Elimination works by combining the equations to remove one variable.

The $y$-terms are $+y$ and $-3y$. If we multiply the first equation by $3$, the $y$-coefficients will be $+3y$ and $-3y$, which are opposites:

Now write this new equation together with the second original equation:

Add these equations term by term:

So $14x = 56$, which gives $x = 4$.

Now substitute $x = 4$ into either original equation to find $y$. Using $4x + y = 22$:

This simplifies to:

Subtract $16$ from both sides:

We found $x = 4$ and $y = 6$, so the ordered pair is $(4,6)$.

Check in the second equation to be sure:

Both equations are true with $(4,6)$, so this is the correct solution.