# How do you solve 3y = -(1/2)x + 2 and y = -x + 9 using substitution?

Apr 2, 2018

$y = - 1$

$x = 10$

#### Explanation:

Substitute $y = - x + 9$ in equation 1: $3 y = - 0.5 x + 2$

$3 \left(- x + 9\right) = - 0.5 x + 2$

$- 3 x + 27 = - 0.5 x + 2$

$- 3 + 0.5 = 2 - 27$

$- 2.5 x = - 25$

The minus signs cancel each other

$2.5 x = 25$

$x = 10$

Now substitute $x = 10$ in equation 2: $y = - x + 9$

$y = - 10 + 9$

$y = - 1$

Apr 2, 2018

x = 10; y = -1

#### Explanation:

Substituting a formula into another essentially means, to set one formula equal to a variable and then inserting the formula into the other formula. Though this might seem complicated, this can be done easily with these equations:
$3 y = \left(\frac{- 1}{2}\right) x + 2$
$y = - x + 9$
$3 \left(- x + 9\right) = \left(\frac{- 1}{2}\right) x + 2$
$- 3 x + 27 = \left(\frac{- 1}{2}\right) x + 2$

Now rearrange the equation to collect like terms on either sides.
1) multiply both sides of the equation by 2 to simplify the situation.
$- 6 x + 54 = - 1 x + 4$

2) add $1 x$ to both sides, to eliminate the x on the right side
$- 6 x \left(+ x\right) + 54 = - 1 x \left(+ x\right) + 4$
$- 5 x + 54 = 4$

3) subtract $54$ from both sides
$- 5 x + 54 \left(- 54\right) = 4 \left(- 54\right)$
$- 5 x = - 50$

4) now divide both sides of the equation by $- 5$
$\frac{- 5 x}{-} 5 = \frac{- 50}{-} 5$
$x = 10$

Now just use this value in one of the initial equations.
$y = - x + 9$
$y = - \left(10\right) + 9$
$y = - 1$