SOLUTION: the soloution of the system of equations below
y=5-3x
4x-5y=13
how do i solve for x and y
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Question 147780: the soloution of the system of equations below
y=5-3x
4x-5y=13
how do i solve for x and y
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y=5-3x
4x-5y=13
-----------
Rearrange:
3x + y = 5
4x -5y = 13
-------------
Again:
15x + 5y = 25
4x - 5y = 13
--------------
Add the two equations to get:
19x = 38
x = 2
--------
Substitute into y = 5-3x to solve for "y":
y = 5-3*2 = -1
===================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:
Start with the first equation.
Rearrange the terms.
-------------------------------------------
Now plug in into the second equation.
Distribute.
Combine like terms on the left side.
Add to both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
-------------------------------------------
Since we know that , we can use this to find .
Go back to the first equation.
Plug in .
Simplify.
So the answer is and .
This means that the system is consistent and independent.
Notice when we graph the equations, we see that they intersect at )
. So this visually verifies our answer.
Graph of (red) and (green)
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