Solve the Simultaneous Equations:

do you have any differential equations?

 

2xy+y=10
x+y=4

to solve for y in the bottom equation, subtract x from both sides..... you get x+y-x=4-x, or y=4-x

plug in 4-x into the top equation for y, you get 2x(4-x)+(4-x)=10

8x-2x^2+4-x=10, subtract 10 from both sides , you get
8x-2x^2+4-x-10=0, add the x's to the single power, and you get
7x-2x^2+4-10=0, add the digits together, you get
7x-2x^2-6=0, arrange the equation to decreasing powers, you get
-2x^2=7x-6=0.

factor equation.....

(-2x+3)(x-2)=0....... so, x-2=0 or -2x+3=0, because multiplying anything by 0=0

x-2=0
add 2 to both sides of equation, and you get x=2, if x=2, then y has to equal 2, from plugging 2 into both equations at the beginning..... 2+y=4, y=4-2, y=2 and 4y+y=10, 5y=10, y=10/5,y=2

therefore x=2 and y=2 is one answer......

-2x+3=0
subtract 3 from both sides you get -2x=-3, divide both sides by 2, you get x=-3/-2, or 3/2, so x=3/2
if x=3/2 and you plug into both of the first equations, you get 3/2+y=4, or y=4-3/2, or y=8/2-3/2, which is y=5/2. 2(3/2)y+y=10, 3y+y=10, 4y=10, y=10/4 or y=5/2

so therefore x=3/2 and y=5/2

so both answers you get is x=2, y=2 and/or x=3/2,y=5/2