How I solve $-2x + 7y + 6 = 20$?

Question

I've been having trouble trying to figure out this linear equation. I only know how to calculate with two variables and no constant, I'm not good at figuring out problems with new "formats" if that's the right word.

I tried subtracting $6$ from both sides, but I don't think that's the right way to do it. I think I'm supposed to subtract $7y$ from both sides? Could you help me learn how to graph and solve this equation?

Answer 1

One of the most common way to graph a function like this is to write it in what is known as slope-intercept form. Slope-intercept form is of the form

$$y=mx+b,$$

where $m$ is the slope, and $b$ is the $y$-intercept. For your problem, we need to solve for $y$:

\begin{align*} -2x+7y+6&=20\\ -2x+7y&=14&\text{by subtracting $6$ to both sides}\\ 7y&=2x+14&\text{by adding $2x$ to both sides}\\ y&=\frac27x+2&\text{by dividing by $7$ on both sides} \end{align*}

This is an equation of a line in slope-intercept form. The slope is $2/7$ and the $y$-intercept is $2$.

To graph it, first plot the $y$-intercept, which is $(0,2)$. To find the next point on our line, we use the slope. You may have heard of "slope is rise over run". In our case, the slope is $2/7$, so our "rise" is $2$, and our "run" is $7$. That is, starting from $(0,2)$, we go up by $2$, and go to the right by $7$, giving us a second point of $(7,4)$. Connecting $(0,2)$ and $(7,4)$ gives us our line.

Answer 2

By subtracting 6 from both sides you will get: -2x + 7y = 14.

To plot this equation on the graph, assume any value of one of the variables and find the other.

Assume x=0, then you will get 7y = 14. Therefore y = 2. So, First point becomes (0, 2).

Similarly assume y=0, then you will get -2x=14. Therefore x=-7. So second point becomes (-7, 0)

Connect these two points on the x-y plane.

You can choose and other value of x or y, you will get the resultant point on the graph of your equation.