Question

Solve
5/x+y - 2/x-y = -1 and 15/x+y + 7/x-y = 10
Using cross-multiplication method.

Answer 1

Answer:

x = 3 and y = 2

Step-by-step explanation:

Start by multiplying the first equation by "-3" so we can cancel the term with denominator (x+y) when we combine:

$\frac{(-3)\,5}{x+y} -\frac{(-3)\,2}{x-y} =(-3)(-1)\\\frac{-15}{x+y} +\frac{6}{x-y} =3$

which now added term by term to the second equation gives:

$\frac{-15}{x+y} +\frac{6}{x-y} =3\\\frac{15}{x+y} +\frac{7}{x-y} =10\\ \\\frac{13}{x-y} =13$

Now we solve for x-y by cross multiplying:

$\frac{13}{13}=x-y\\ x-y=1\\x=y+1$

Now we use this substitution for x  back in the first equation to solve for the unknown y:

$\frac{5}{(y+1)+y} -\frac{2}{(y+1)-y} =-1\\\frac{5}{2y+1} -2=-1\\\frac{5}{2y+1}=1\\5=2y+1\\4=2y\\y=2$

and now that we know that y = 2, we use the substitution equation to solve for x:

$x=y+1\\x=2+1\\x=3$