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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:


system%28y=5-3x%2C4x-5y=13%29


y=5-3x Start with the first equation.


y=-3x%2B5 Rearrange the terms.


-------------------------------------------


4x-5%28-3x%2B5%29=13 Now plug in y=-3x%2B5 into the second equation.


4x%2B15x-25=13 Distribute.


19x-25=13 Combine like terms on the left side.


19x=13%2B25 Add 25 to both sides.


19x=38 Combine like terms on the right side.


x=%2838%29%2F%2819%29 Divide both sides by 19 to isolate x.


x=2 Reduce.


-------------------------------------------


Since we know that x=2, we can use this to find y.


y=5-3x Go back to the first equation.


y=5-3%282%29 Plug in x=2.


y=-1 Simplify.

So the answer is x=2 and y=-1.


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 y=5-3x (red) and 4x-5y=13 (green)