Question 219·Medium·Algebra

Rearrange the simpler equation so it says $y =$ (something involving $x$). Be careful with negative signs when you move terms across the equals sign.

Take your expression for $y$ and plug it into the other equation. Then solve the resulting equation to find $x$, and use that $x$-value to get $y$.

In Desmos, type 5x+3y=1 on one line and 2x-y=7 on another line. Desmos will graph both as lines in the coordinate plane.

Adjust the view (zoom or drag) until you see where the two lines cross. Tap or click on the intersection point; Desmos will show its coordinates $(x, y)$.

Read the y-coordinate of the intersection point shown by Desmos. That y-value is the answer to the question.

Look at the system:

The second equation, $2x - y = 7$, is easiest to solve for $y$ because $y$ has a coefficient of $-1$.

From $2x - y = 7$:

• Subtract $2x$ from both sides: $-y = 7 - 2x$.
• Multiply both sides by $-1$: $y = 2x - 7$.

Now you have $y$ written in terms of $x$.

Substitute $y = 2x - 7$ into the first equation $5x + 3y = 1$:

Now simplify:

So the $x$-value of the solution is $2$.

Use $y = 2x - 7$ and plug in $x = 2$:

Therefore, the value of $y$ is $-3$.