Question 144·Medium·Algebra

Take the expression for $y$ from the simpler equation and plug it into $y$ in the other equation. After you do this, you should have an equation with only $x$.

Once you find the value of $x$, plug it back into the easier equation $y = x - 1$ to compute $y$.

First rewrite the equation $2y = 3x + 6$ in slope-intercept form by dividing both sides by 2: $y = \tfrac{3}{2}x + 3$. In Desmos, type the two equations as:

• y = (3/2)x + 3
• y = x - 1

Look at the graph where the two lines intersect. Click on that intersection point; Desmos will show its coordinates $(x, y)$. The $y$-value of this intersection point is the answer to the question.

Notice the second equation is already solved for $y$:

This makes substitution the fastest method: replace $y$ in the first equation with the expression $x - 1$.

Start with the first equation:

Substitute $y = x - 1$ into it:

Now you have an equation in just one variable, $x$.

Simplify and solve the equation from Step 2:

Move all $x$-terms to one side and constants to the other:

So $x = -8$.

Use the equation $y = x - 1$ with $x = -8$:

Therefore, the value of $y$ is $-9$.