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Comment on 3 Equations with 3 Unknowns
At the step when substituting
If you show me your work, I
If you show me your work, I can probably help to identify the problem.
You can only use systems of
You can still apply some of
You can still apply some of same principles from solving 3 linear equations to solving other systems.
Here is the elimination
w - 2x +3y = 13 --- (1)
2w + x -4y = -14 ----(2)
3w - x +2y = 8 ----(3)
Add (2) and 3 to eliminate x --> 5w - 2y = -6
Multiply (2) by 2 and add to (1) to elimniate
x --> 5w - 5y = -15
The resulting two equations with 2 unknowns are:
5w - 2y = -6 --- (4)
5w - 5y = -15 --- (5)
Subtract (5) from (4) to to get: 3y = 9 --> y = 3
Substitute the value of y in (4): 5w -2(3) = -6 --> w = 0
substitute the values of w and y in (3) to solve for x:
3(0) - x +2(3) = 8 --> -x = 2 --> x = -2
Solution: w = 0, x = -2, y = 3
Great work!
Great work!
I have tried so many times to
Glad to help!
Glad to help!
GIVEN:
w - 2x + 3y = 13 ----(1)
2w + x - 4y = -14 ----(2)
3w - x + 2y = 8 ----(3)
Add equations (2) and (3) to get: 5w - 2y = -6 ----(4)
Take equation (2) and multiply both sides by 2 to get: 4w + 2x - 8y = -28
Now add this equation to equation (1), w - 2x + 3y = 13
We get: 5w - 5y = -15 ----(5)
We now have: 5w - 2y = -6 ----(4)
And we have: 5w - 5y = -15 ----(5)
Subtract (5) from (4) to get 3y = 9
Solve: y = 3
Once we know that y = 3, we can take equation (4) and replace y with 3
When we do this, we get: 5w - 2(3) = -6
Simplify: 5w - 6 = -6
Solve: w = 0
Once we know that w = 0 and y = 3, we can plug these values into any equation and then solve for x.
When we do this, we get x = -2
Does that help?
Cheers,
Brent
The above solution uses the
The above solution uses the Elimination method.
Here's a solution that uses the Substitution method.
w - 2x + 3y = 13 ----(1)
2w + x - 4y = -14 ----(2)
3w - x + 2y = 8 ----(3)
Take (1) and solve for w to get: w = 2x - 3y + 13 ----(4)
Now take (2) and replace w with 2x - 3y + 13
We get: 2(2x - 3y + 13) + x - 4y = -14
Expand: 4x - 6y + 26 + x - 4y = -14
Simplify: 5x - 10y = -40
Divide both sides by 5 to get: x - 2y = -8 ---(5)
Also take (3) and replace w with 2x - 3y + 13
We get: 3(2x - 3y + 13) - x + 2y = 8
Expand: 6x - 9y + 39 - x + 2y = 8
Simplify: 5x - 7y = -31 ---(6)
We now have two equations with 2 variables:
x - 2y = -8 ---(5)
5x - 7y = -31 ---(6)
Let's use the Substitution method to solve this system.
Take (5) and solve for x to get: x = 2y - 8 + ---(7)
Now take (6) and replace x with 2y - 8
We get: 5(2y - 8) - 7y = -31
Expand: 10y - 40 - 7y = -31
Simplify: 3y = 9
Solve: y = 3
Now we can determine the values of x and y
Take (7) and replace y with 3 to get: x = 2(3) - 8 = 6 - 8 = -2
So, x = -2
Now take (4) and replace x and y with -2 and 3
We get: w = 2(-2) - 3(3) + 13
= -4 - 9 + 13
= 0
So, w = 0
Cheers,
Brent
How did you get 5x as an
Good catch, Navin!
Good catch, Navin!
When I first simplified 6x - 9y + 39 - x + 2y = 8, I incorrectly got 7x - 7y = -31.
I SHOULD have simplified it to be 5x - 7y = -31
I've fixed the error.
Cheers,
Brent