How do you solve the following system using substitution?: 4x + 5y = 6, y = 2x - 10

1 Answer
Oct 22, 2015

$x = 4$, $y = - 2$.

Explanation:

From the second equation, we know that $y = 2 x - 10$. So we can susbtitute every occurrence of $y$ with $2 x - 10$ in the first equation:

$4 x + 5 \textcolor{g r e e n}{y} = 6 \to 4 x + 5 \textcolor{g r e e n}{\left(2 x - 10\right)} = 6$.

Expanding, we have $4 x + 10 x - 50 = 6$. Isolating the $x$ term, we have

$14 x = 56$, which we solve for $x$ finding $x = \frac{56}{14} = 4$.

Once we know the value of $x$, we obtain $y$ by substituing in the second equation (for example):

$y = 2 x - 10 \to y = 2 \cdot 4 - 10 = - 2$.

Note that we could have chosen the first equation:

$4 x + 5 y = 6 \to 4 \cdot 4 + 5 y = 6 \to 5 y = - 10 \to y = - 2$.