Answer:
Explanation:
To solve the system of equations:
Ax - By = 24
Bx + Ay = 31
We can use the method of substitution. Here's how:
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x in terms of y:
Ax - By = 24
Ax = By + 24
x = (By + 24)/A
2. Substitute the expression for x into the second equation:
Bx + Ay = 31
B((By + 24)/A) + Ay = 31
3. Simplify the equation by distributing and combining like terms:
(B^2y + 24B)/A + Ay = 31
4. Multiply through by A to eliminate the fraction:
B^2y + 24B + A^2y = 31A
5. Combine like terms:
(B^2 + A^2)y + 24B = 31A
6. Solve for y by isolating the y term:
(B^2 + A^2)y = 31A - 24B
y = (31A - 24B)/(B^2 + A^2)
7. Substitute the value of y back into the expression for x from step 1:
x = (By + 24)/A
x = [(B(31A - 24B))/(B^2 + A^2)] + 24/A
So, the solution to the system of equations is:
x = [(B(31A - 24B))/(B^2 + A^2)] + 24/A
y = (31A - 24B)/(B^2 + A^2)