Question 139·Easy·Algebra

If you add the left sides and the right sides of the two equations, what happens to $+y$ and $-y$?

After $y$ cancels, you will have an equation with only $x$. Solve that equation to find the value of $x$.

In Desmos, type x + y = 10 on one line and x - y = 2 on another line. Desmos will graph both lines.

Look for the point where the two lines intersect. Tap or click that intersection point so Desmos shows its coordinates $(x, y)$.

Read the $x$-coordinate of the intersection point. That value is the solution for $x$ in the system.

Notice that one equation has $+y$ and the other has $-y$. If we add the two equations, the $y$ terms will cancel:

On the left side, $+y$ and $-y$ cancel, leaving:

Now solve the simpler equation $2x = 12$ by dividing both sides by $2$:

This gives a single value for $x$.

From the division, we get:

Quick check (optional): If $x = 6$, then from $x + y = 10$ we get $6 + y = 10$, so $y = 4$. Check in the second equation: $6 - 4 = 2$, which is true. So the value of $x$ is $6$.