If you multiply the second equation by $2$, what does the coefficient of $x$ become? Write that new equation under the first one.

With matching $x$-coefficients, subtract one equation from the other. What expression do you get for the $y$-terms, and what do you get on the right side?

You should now have an equation of the form $10y = \text{(some number)}$. Solve this simple one-step equation for $y$.

Type 6x - 2y = 14 on one line and 3x + 4y = 2 on the next line. Desmos will graph both lines on the coordinate plane.

Click on the point where the two lines intersect. Desmos will display the coordinates $(x,y)$ of this point; the second number is the value of $y$ that solves the system.

You are given a system of two linear equations and asked for the value of $y$ in the ordered pair $(x,y)$ that satisfies both equations:

You do not need to find $x$ if you can solve directly for $y$.

Notice the coefficients of $x$ in the two equations are $6$ and $3$. If we multiply the second equation by $2$, the coefficient of $x$ will also be $6$.

Multiply the entire second equation by $2$:

Now you have a new system:

with matching $x$-coefficients.

Subtract the first equation from the second to eliminate $x$:

• Left side:
  • $(6x + 8y) - (6x - 2y)$
• Right side:
  • $4 - 14$

Compute each part:

So you get a single equation in $y$:

Solve $10y = -10$ by dividing both sides by $10$:

So, in the solution $(x,y)$ to the system, the value of $y$ is $-1$.