Question

2x+3y=1 and y=-2 - 9 solve using linear combination method. Please explain steps.

Answer 1

Answer:

$x=17$

Step-by-step explanation:

$2x+3y=1$

$y=-2-9$

• In order to combine these two equations, an idea you need to keep in mind is finding a way of setting these equations as equal to each other. I saw that each equation shared a common value, $y$. In this case, we need to isolate $y$ in the first equation so that both equations $=y$.

$2x+3y=1$

$3y=-2x+1$

$\frac{3y}{3}=\frac{-2x+1}{3}$

$y=-\frac{2}{3}x+\frac{1}{3}$

• With this, we now know that both $-2-9$ and $-\frac{2}{3}x+\frac{1}{3}$ are equal to $y$, so we can set them equal to each other.

$y=-\frac{2}{3}x+\frac{1}{3}$

$y=-11$

$-\frac{2}{3}x+\frac{1}{3}=-11$

• Reply to this if anything I'm saying or doing is confusing in any way, or if you find a mistake. :) Solve for $x$.

$-\frac{2}{3}x+\frac{1}{3}=-11$

$-\frac{2}{3}x=-11-\frac{1}{3}$

$-\frac{2}{3}x =-\frac{33}{3}-\frac{1}{3}$

$-\frac{2}{3}x =-\frac{34}{3}$

$-\frac{2}{3}x(-\frac{3}{2})=-\frac{34}{3}(-\frac{3}{2})$

$x=\frac{102}{6}=17$

$x=17$

• Hopefully this answer is correct AND makes sense in terms of how I achieved it. Again, reply to this with any questions or mistakes I made and I'll do my best to answer or fix them.