Question

Solve the following system of equations: −2x + y = 1 −4x + y = −1

Answer 1

Make one of the variables drop out.

I'd go for the y since it's easiest in this problem.

Time the top equation by -1.

This changes the system to:
$2x + - y = 1$
$- 4x + y = - 1$
Add the equations.

$2x + - 4x = - 2x$
$- y + y = 0$
$1 + - 1 = 0$
The equation would be:
$- 2x + 0 = 0$
Or simply:
$- 2x = 0$
Solve for x by dividing.
$x = 0 \div - 2$
$x = 0$
Then, plug x into one of the original equations to find y.

I'm going to use the first one since the numbers are smaller, but you CAN use either.

$- 2(0) + y = 1$
$0 + y = 1$
$y = 1$
Put these into an ordered pair.

(0,1)

That is your answer.

Hope this helped!

:)

Answer 2

Explanation:

Solve −2x+y=1 for y

y=2x+1

Substitute 2x+1 for y in −4x+y=−1

x=1

Substitute 1 for x in y=2x+1

y=3

Final answer:

x=1 y=3