How do you solve the following system?: $-x -2y =1, x -y = -1$

Question

4323 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-12T12:25:56

See the entire solution process below:

Step 1) Solve the second equation for $x$ :

$x - y = -1$

$x - y + color(red)(y) = -1 + color(red)(y)$

$x - 0 = -1 + y$

$x = -1 + y$

Step 2) Substitute $-1 + y$ for $x$ in the first equation and solve for $y$ :

$-x - 2y = 1$ becomes:

$-(-1 + y) - 2y = 1$

$1 - y - 2y = 1$

$1 - 1y - 2y = 1$

$1 - 3y = 1$

$-color(red)(1) + 1 - 3y = -color(red)(1) + 1$

$0 - 3y = 0$

$-3y = 0$

$(-3y)/color(red)(-3) = 0/color(red)(-3)$

$(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = 0$

$y 0$

Step 3) Substitute $0$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$ :

$x = -1 + y$ becomes:

$x = -1 + 0$

$x = -1$

The solution is: $x = -1$ and $y = 0$ or $(-1, 0)$

How do you solve the following system?: -x -2y =1, x -y = -1-x -2y =1, x -y = -1