After distributing, you should get a simpler system in $x$ and $y$. Think about using elimination (or substitution) to solve the two linear equations.

Look at the coefficients of $x$ and $y$ in the simplified equations. Which variable can you eliminate more easily by multiplying the equations and adding or subtracting them?

Once you find $x$ and $y$, remember the question asks for $x+y$, not just $x$ or just $y$. Add the two values carefully.

In Desmos, type the first equation exactly as given: 2(7x-5y)-(4x+3y)=59. Desmos will graph this relation as a line.

On a new line, type the second equation: 3(4x+3y)+(7x-5y)=26. This will graph the second line.

Adjust the viewing window if needed so both lines are visible. Click on their point of intersection; Desmos will display the coordinates $(x,y)$ of that point.

Take the $x$-coordinate and $y$-coordinate of the intersection point you found in Desmos and add them together to get the value of $x+y$.

First, remove the parentheses by distributing.

For the first equation:

Combine like terms:

So the first equation becomes:

For the second equation:

Combine like terms:

So the second equation becomes:

Now the simplified system is:

Eliminate $y$ by making the $y$-coefficients opposites.

Multiply the first equation by $4$ and the second equation by $13$ so that the $y$-terms become $-52y$ and $+52y$:

• First equation $\times 4$:

• Second equation $\times 13$:

Now add these two new equations:

The $y$-terms cancel:

Solve for $x$ by dividing both sides by $287$:

Substitute $x=2$ into either simplified equation. Using $19x+4y=26$:

So:

Subtract $38$ from both sides:

Divide by $4$:

Now that $x=2$ and $y=-3$, add them to find $x+y$:

So the value of $x+y$ is $-1$.