How do you solve 9x+5y=-21 and -2x+y=11 using substitution?

Jul 31, 2016

$x = - 4$, $y = 3$. Solve the second equation for $y$ and put the answer in terms of $x$ into the first equation.

Explanation:

$- 2 x + y = 11$.

When you are trying to find something that is lost always work backwards. PEMDAS backwards become PE SADM
(if you lose something in PE you are a sad member of humanity.
so the opposite of $- 2 x = + 2 x$

Add $+ 2 x$ to both sides of the equation

$- 2 x + 2 x + y = y + 2 x$

$- 2 x + 2 x = 0$

leaving

$y = 2 x + 11$

Now substitute $+ 2 x + 11$ into the first equation for $y$ giving

$9 x + 5 \left(+ 2 x + 11\right) = - 21$

Remember PE always comes first. Use the distributive property to multiply $5 \times \left(+ 2 x\right)$ and $5 \times 11$. This gives

$9 x + 10 x + 55 = - 21$

You are trying to find x which you somehow lost so you are a SAD M. Subtract $55$ from both sides.

$+ 55 - 55 = 0 \text{ }$ and $\text{ } - 21 - 55 = - 76$

leaving you with

$19 x = - 76$

SA are gone so now you have to Divide. (D M) divide both sides by $19$.

$\frac{19 x}{19} = - \frac{76}{19}$

$\frac{19}{19} = 1 \text{ }$ and $\text{ } - \frac{76}{19} = - 4$. so

$x = - 4$

Substitute $- 4$ into the first equation

$y = 11 + 2 \left(- 4\right)$

$y = 11 + \left(- 8\right)$

$y = 3$

If you remember that when you are trying to find something lost you are a SAD M and you won't be sad.