# Solve the system of equations by any​ method: substitution, or elimination? y=2x-4y and 4x+1=10y+7

## substitution

No solution - the two lines are parallel

#### Explanation:

Let's use substitution:

Equation 1:

$y = 2 x - 4 y$

$5 y = 2 x \implies 10 y = 4 x$

We can substitute that into equation 2:

$4 x + 1 = 10 y + 7$

$10 y + 1 = 10 y + 7$

And we run into a problem with the question - these equations have no joint solution.

We can graph the two of them to see:

Equation 1:

$10 y = 4 x \implies y = \frac{2}{5} x$

Equation 2:

$10 y = 4 x - 6 \implies y = \frac{2}{5} x - \frac{3}{5}$

These two equations describe 2 parallel lines:

graph{(y-2/5x)(y-2/5x+3/5)=0}