# How do you solve this system of equations using the substitution method x- y = 1 and 4x + 9y = - 87?

Aug 13, 2018

$y = - 7$
$x = - 6$

#### Explanation:

Given -

$x - y = 1$ ----------------(1)
$4 x + 9 y = - 87$ ----------(2)
Solve equation (1) for $x$
$x = 1 + y$
Substitute $x = 1 + y$ in equation (2)
$4 \left(1 + y\right) + 9 y = - 87$
$4 + 4 y + 9 y = - 87$
$13 y = - 87 - 4 = - 91$
$y = \frac{- 91}{13} = - 7$

$y = - 7$

Substitute $y = - 7$ in equation (1)

$x - \left(- 7\right) = 1$
$x + 7 = 1$
$x = 1 - 7 = - 6$

$x = - 6$

Aug 13, 2018

$x = - 6 \mathmr{and} y = - 7$

#### Explanation:

Here ,

$x - y = 1 \implies x = y + 1. \ldots . \to \left(1\right)$

$4 x + 9 y = - 87. \ldots \ldots \ldots \ldots \ldots . \to \left(2\right)$

Substitute value of $x$ from$\left(1\right)$ into $\left(2\right)$

$4 \left(y + 1\right) + 9 y = - 87$

$4 y + 4 + 9 y = - 87$

$13 y = - 91$

:.color(red)(y=-7

Subst. color(red)(y=-7 into (1)

x=color(red)(-7)+1=>color(blue)(x=-6

Hence , $x = - 6 \mathmr{and} y = - 7$