How do you solve the following system: $-8x+2y=4 , 4x+y=10$ ?

Question

1576 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-24T14:28:44

See the entire solution process below:

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

$4x + y = 10$

$4x - 4x + y = 10 - 4x$

$0 + y = 10 - 4x$

$y = 10 - 4x$

Step 2) Substitute $color(red)(10 - 4x)$ for $y$ in the first equation and solve for $x$ :

$-8x + 2(color(red)(10 - 4x)) = 4$

$-8x + 20 - 8x = 4$

$-16x + 20 = 4$

$-16x + 20 - color(red)(20) = 4 - color(red)(20)$

$-16x + 0 = -16$

$-16x = -16$

$(-16x)/color(red)(-16) = (-16)/color(red)(-16)$

$(color(red)(cancel(color(black)(-16)))x)/cancel(color(red)(-16)) = 1$

$x = 1$

Step 3) Substitute $color(red)(1)$ for $x$ in the solution to the second equation at the end of Step 1 and calculate $y$ :

$y = 10 - (4 xx color(red)(1))$

$y = 10 - 4$

$y = 6$

The solution is $x = 1$ and $y = 6$ or (1, 6)

How do you solve the following system: -8x+2y=4 , 4x+y=10 -8x+2y=4 , 4x+y=10 ?