Step-by-step explanation:
equation 1 : -3x + 4y = -18
equation 2: x = -2y -4
transformed equation 2: x + 2y = -4
-3x + 4y = -18
x + 2y = -4
By elimination means we have to make one variable equal to zero or we have to take one variable out of the whole equation.
Let's eliminate the variable x. To do so, let's multiple the second equation to +3. Therefore,
-3x + 4y = -18
(3)x + (3)(2y) = (3)(-4)
-3x + 4y = -18
3x + 6y = -12
Now that both equations have the same value of x but different signs, we can now eliminate x by adding the two equations.
-3x + 4y = -18
<u>3x + 6y = -12</u>
<u> </u> 0 + 10y = -30
Dividing both sides by 10, we have y = -3.
Now that we have the value of y, we can just substitute the value of y into either one of the equation OR we can do the process again but this time we need to eliminate y to find the value of x.
-3x + 4y = -18
x + 2y = -4
To eliminate y, we need to multiply the second equation by -2.
-3x + 4y = -18
(-2)x + (-2)2y = -4(-2)
-3x + 4y = -18
-2x - 4y = 8
Now that we have the same values but different signs of y, we can now add the two equations again.
-3x + 4y = -18
<u>-2x - 4y = 8</u>
-5x + 0 = -10
Dividing both sides by -5, we have x = 2.
CHECKING:
Let's take the second original equation,
x = -2y -4
Let's substitute the values we have found into the equation:
2 = -2(-3) - 4
2= 6 - 4
2 = 2
Both sides of the equation produced the same values. Therefore, the values are correct.
