How do you solve the system $- 4 x + y = 6$ $-4x+ y =6$ and $- 5 x - y = 21$ $-5x - y =21$ by substitution?

Question

11325 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-21T08:12:00

May 21, 2015

Answer 2 · 2015-05-21T08:14:59

$- 4 x + y = 6$ $-4x+ y =6$ ----------(1)
$- 5 x - y = 21$ $-5x - y =21$ ----------(2)

We can transpose $- 4 x$ $-4x$ in the first equation to the right hand side:

$y = 4 x + 6$ $y = 4x + 6$ ------(3)

Substituting $y$ $y$ from the third equation into the second one gives us:

$- 5 x - (4 x + 6) = 21$ $- 5x - (4x+6) = 21$

$- 5 x - 4 x - 6 = 21$ $-5x - 4x - 6 = 21$

$- 9 x - 6 = 21$ $-9x - 6 = 21$

$- 9 x = 21 + 6$ $-9x = 21+6$

$- 9 x = 27$ $-9x = 27$

Dividing both sides by $- 9$ $-9$ will give us:

$(cancel(-9)x)/cancel(-9) = 27/-9$

$color(green)(x = -3$

Substituting $x = -3$ in the third equation will give us :

$y = 4(-3) + 6$

$y = -12 + 6$

$color(green)( y = -6$

The solution to both these equations : $x = -3; y = -6$

Verify :

Substitute the values of $x and y$ in both the equations to see if they are satisfied

How do you solve the system -4x+ y =6−4x+y=6-4x+ y =6 and -5x - y =21−5x−y=21-5x - y =21 by substitution?