Question 214·Easy·Algebra

What happens if you add the two equations together, left side with left side and right side with right side? Which variable disappears?

Once you find a value for $x$, plug it back into either original equation to solve for $y$.

In Desmos, type 3x + y = 7 on one line and x - y = 1 on another line so both lines are graphed.

Look for the point where the two lines cross. You can tap or click near the crossing point and Desmos will display its coordinates.

The coordinates of that intersection are the $(x, y)$ solution to the system. Compare those coordinates to the answer options and choose the matching ordered pair.

Look at the system:

• $3x + y = 7$
• $x - y = 1$

Notice that the coefficients of $y$ are $+1$ and $-1$. If you add the two equations, the $y$ terms will cancel out, which makes it easy to solve for $x$.

Add the left sides and the right sides:

• Left side: $(3x + y) + (x - y) = 3x + x + y - y = 4x$
• Right side: $7 + 1 = 8$

So you get the equation $4x = 8$. Divide both sides by 4:

• $x = 2$.

Now plug $x = 2$ into either original equation. Use $x - y = 1$:

• $2 - y = 1$
• Subtract 2 from both sides: $-y = -1$
• Multiply both sides by $-1$: $y = 1$

So the solution that satisfies both equations is $(x, y) = (2, 1)$.