How do you solve this set of linear equations: 7x - 5y = 9; y = x - 1?

Nov 28, 2016

$\left\{\begin{matrix}x = 2 \\ y = 1\end{matrix}\right.$

Explanation:

$\left\{\begin{matrix}7 x - 5 y = 9 \\ y = x - 1\end{matrix}\right.$

Substitute $x - 1$ for $y$ in the first equation

$7 x - 5 \left(x - 1\right) = 9$

Multiply out the brackets

$7 x - 5 x + 5 = 9$

Subtract $5$ from both sides

$7 x - 5 x = 4$

$2 x = 4$

$x = 2$

Then

$y = x - 1$

$y = 2 - 1$

$y = 1$

To check, substitute the answers into the first equation

$7 x - 5 y = 9$

$14 - 5 = 9$