Ok, I tried watching a video on how to solve a system by substitution. But I feel like I did it wrong, so can someone check my work and show/ tell me where I went wrong.
So the system by substitution
-2x-3y=-2
Y=2x+6
First I combined my 2 equations but without y so I’d have 1 equation
-2x-3(2x+6)=-2
Then I multiplied 3 with 2 and 6 and got
-2x-6x+18=-2
Then added -2 and 6 and got
-8x+18=-2
(Then I did some more stuff the man in the video did)
-8x+18=-2
-18-18
And I ended up with this -8/8x=-16/18=-8/9
Meanwhile the man in the video I guess did his correctly and found his x mean while I’m confused and lost. So can someone help me?...
Your error is in this line: -2x-6x+18=-2
should have been -18, since (-3)(+6) = -18
so ..
-2x-6x-18=-2
-8x - 18 = -2
-8x = 18-2
-8x = 16
x = -2
sub back into y = 2x+6
= 2(-2) + 6
= 2
x = -2, y = 2
It looks like you made a mistake in the step where you combined your two equations.
Let's go through the steps of solving the system by substitution again to identify where the error occurred.
Given the system of equations:
-2x - 3y = -2 ........ (Equation 1)
y = 2x + 6 ........ (Equation 2)
To solve by substitution, we substitute Equation 2 into Equation 1, replacing y with its equivalent expression in terms of x.
Start by substituting y in Equation 1:
-2x - 3(2x + 6) = -2
Now, distribute the -3 to each term inside the parentheses:
-2x - 6x - 18 = -2
Combine like terms on the left-hand side:
-8x - 18 = -2
Next, add 18 to both sides of the equation to isolate x:
-8x = -2 + 18
-8x = 16
To find x, divide both sides of the equation by -8:
x = 16 / -8
x = -2
Now that we have the value of x, we can substitute it back into Equation 2 to find the corresponding y-value:
y = 2(-2) + 6
y = -4 + 6
y = 2
Thus, the solution to the system of equations is x = -2 and y = 2.
It seems like the mistake you made was when you subtracted 18 on both sides of the equation after reaching -8x + 18 = -2. Instead of subtracting, you should have added 18 to both sides to isolate the variable -8x.