Question

7 + 2y = 8x 3x - 2y = 0 Solve the system of equations by substitution. (70/3, 140/9) (7/5, 21/10) no solution coincident

Answer 1

So we have the system of equations:
$7+2y=8x$ equation (1)
$3x-2y=0$ equation (2)

To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for $x$ in equation (2):
$3x-2y=0$
$3x=2y$
$x= \frac{2}{3}y$ equation (3)

Replacing equation (3) in equation (1):
$7+2y=8x$
$7+2y=8( \frac{2}{3} y)$
$7+2y= \frac{16}{3} y$
$7= \frac{10}{3} y$
$y= \frac{7}{ \frac{10}{3} }$
$y= \frac{21}{10}$ equation (4)

Replacing equation (4) in equation (3):
$x= \frac{2}{3}y$
$x=( \frac{2}{3} )( \frac{21}{10} )$
$x= \frac{7}{5}$

We can conclude that the solution of our system of equations is (7/5, 21/10)