SOLUTION: I am trying to do systems of equations for algebra 2 I am stuck on the first problem which is 5x+4y=6 -2x-3y= -1 can you help me out so far I have subtracted 5x -

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Question 985492: I am trying to do systems of equations for algebra 2 I am stuck on the first problem which is 5x+4y=6
-2x-3y= -1 can you help me out so far I have subtracted 5x - 2x and got 3x and I subtracted 3y from 4y and I have subtracted 6- -1 and got the equation 3x- 1y = 7 I think I cancel out the y value and divide 3x by 3 and 7 divided by 3 but I don't know I'm stuck please help me asap
Found 3 solutions by Alan3354, macston, ThePhysicsMathGuru:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
5x+4y = 6
-2x-3y= -1
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To use elimination, you have to make the coefficients of either x or y match.
To eliminate x:
5x+4y = 6 times 2 --> 10x + 8y = 12
-2x-3y= -1 times 5 -->-10x -15y = -5
------
10x + 8y = 12
-10x -15y = -5
------------------ Add
-7y = 7
y = -1
Sub for y in any equation to find x
5x+4y = 6
5x - 4 = 6
5x = 10
x = 2

Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website!
.
5x+4y=6 Multiply this by 2. This will help get 2 equations with equal x's.
10x+8y=12 Add this below.
.
-2x-3y=-1 Multiply this by 5.
-10x-15y=-5 Add equation from above.
(-10x-15y)+(10x+8y)=-5+12
-7y=7
y=-1 Substitute this in one of the original equations.
5x+4y=6
5x+4(-1)=6
5x-4=6
5x=10
x=2
.
CHECK (Use the other original equation):
-2x-3y=-1
-2(2)-3(-1)=-1
-4+3=-1
-1=-1
.
The answer is (2,-1)

Answer by ThePhysicsMathGuru(3)   (Show Source):
You can put this solution on YOUR website!
5x + 4y = 6 (1)
-2x - 3y = -1 (2)
This set of simultaneous equations can be solved one of three different ways:
1. Using determinates
2. You can solve for x in equation (1) and then plug the value found for x into equation (2) and solve for y. You just have to remember,now you have the solution for y and you have to plug that value back into either equation to get the value for x.
3. Simply multiply both equations by a common value that will allow one of the variables to disappear.
I chose to use the latter.
If you multiply the first equation by 3 and the second by 4 you get the following
15x + 12Y = 18
-8x - 12y = -4
---------------
7x = 14
x = 2
What I did was simply add the two equations together.
Now plug the value for x in either equation and solve. I chose to use the first one.
10 + 4y = 6
4y = -4
y = -1
So our solution is x = 2 and y = -1. One more step we need to verify that we did the computation correctly. Now plug the values for x and y back into each equation and you should get the numbers on the right hand side.
2*5 + 4*(-1) = 6
-2*2 - 3*(-1) = -1
Q.E.D We have not proven that the solution to the equation is x = 1 and y = -1

Now plu