How do you solve the system 3y-8x=24 and 3y+2x=9?

Jul 27, 2016

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

I have taken you just to this point so that you can complete the whole thing.

Explanation:

The trick is to eliminate one of the variables so that you only have one unknown left.

Write as

$\text{ } 3 y - 8 x = 24$
$\text{ "ul(3y+2x=color(white)(2)9) " "larr" Subtract}$
$\text{ } 0 - 10 x = 15$

Multiply both sides by $\left(- 1\right)$

$+ 10 x = - 15$

Divide both sides by 10

$x = - \frac{{\cancel{15}}^{3}}{{\cancel{10}}^{2}} \text{ "larr" Divide top and bottom by 5}$

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

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Now just substitute $\frac{3}{2}$ for $x$ in any of the given equations and solve for $y$

$\textcolor{g r e e n}{\text{I have left that for you to do!}}$