SOLUTION: 7x+3y=4, 5x+9y=10

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 7x+3y=4, 5x+9y=10      Log On


   

Question 167608: 7x+3y=4, 5x+9y=10
Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++7%5Cx+%2B+3%5Cy+=+4%2C%0D%0A++++5%5Cx+%2B+9%5Cy+=+10+%29%0D%0A++We'll use substitution. After moving 3*y to the right, we get:
7%2Ax+=+4+-+3%2Ay, or x+=+4%2F7+-+3%2Ay%2F7. Substitute that
into another equation:
5%2A%284%2F7+-+3%2Ay%2F7%29+%2B+9%5Cy+=+10 and simplify: So, we know that y=1.04166666666667. Since x+=+4%2F7+-+3%2Ay%2F7, x=0.124999999999999.

Answer: system%28+x=0.124999999999999%2C+y=1.04166666666667+%29.

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%287x%2B3y=4%2C5x%2B9y=10%29


-3%287x%2B3y%29=-3%284%29 Multiply the both sides of the first equation by -3.


-21x-9y=-12 Distribute and multiply.


So we have the new system of equations:
system%28-21x-9y=-12%2C5x%2B9y=10%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-21x-9y%29%2B%285x%2B9y%29=%28-12%29%2B%2810%29


%28-21x%2B5x%29%2B%28-9y%2B9y%29=-12%2B10 Group like terms.


-16x%2B0y=-2 Combine like terms. Notice how the y terms cancel out.


-16x=-2 Simplify.


x=%28-2%29%2F%28-16%29 Divide both sides by -16 to isolate x.


x=1%2F8 Reduce.


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


-21x-9y=-12 Now go back to the first equation.


-21%281%2F8%29-9y=-12 Plug in x=1%2F8.


-21%2F8-9y=-12 Multiply.


cross%288%29%28-21%2Fcross%288%29%29-8%289y%29=8%28-12%29 Multiply EVERY term by the LCD 8 to clear the fraction.


-21-72y=-96 Multiply.


-72y=-96%2B21 Add 21 to both sides.


-72y=-75 Combine like terms on the right side.


y=%28-75%29%2F%28-72%29 Divide both sides by -72 to isolate y.


y=25%2F24 Reduce.


======================================

Answer:

So the solutions are x=1%2F8 and y=25%2F24