Solve
x/a-y/b =0
ax+by = a*a + b * b
DUde 1 of u question has been solve check it out it is similiar
x/a-y/b=0
y = bx/a
ax + b(bx/a) = a^2 + b^2
(a^2 + b^2)x = a(a^2 + b^2)
x = a
so, y = b
To solve the system of equations:
1. Start by multiplying the first equation by ab to eliminate the denominators:
ab * (x/a - y/b) = ab * 0
Simplifying this equation gives you:
bx - ay = 0
2. Now we have two equations:
bx - ay = 0 (Equation 1)
ax + by = a^2 + b^2 (Equation 2)
3. We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method in this case.
4. Multiply Equation 1 by a, and Equation 2 by b to make the coefficients of x the same:
abx - a^2y = 0 (Equation 3)
abx + b^2y = a^2 + b^2 (Equation 4)
5. Now we can subtract Equation 3 from Equation 4 to eliminate the term abx:
(abx + b^2y) - (abx - a^2y) = a^2 + b^2 - 0
This simplifies to:
b^2y - (-a^2y) = a^2 + b^2
Rearranging the equation gives you:
b^2y + a^2y = a^2 + b^2
Combining like terms gives:
(b^2 + a^2)y = a^2 + b^2
6. Divide both sides of the equation by (b^2 + a^2) to solve for y:
y = (a^2 + b^2) / (b^2 + a^2)
7. Now substitute the value of y back into Equation 1 to solve for x:
bx - a * ((a^2 + b^2) / (b^2 + a^2)) = 0
Multiply through by (b^2 + a^2) to eliminate the denominator:
b^2x - a(a^2 + b^2) = 0
Distribute the a term:
b^2x - a^3 - ab^2 = 0
Rearrange the equation:
b^2x = a(a^2 + b^2) + ab^2
Combine like terms:
b^2x = a^3 + ab^2 + ab^2
Simplify:
b^2x = a^3 + 2ab^2
Finally, divide both sides by b^2 to solve for x:
x = (a^3 + 2ab^2) / b^2
That's the solution for x and y in terms of a and b, in this system of equations.