solve 43x+67y=-24 67x43y=24
To solve the system of equations:
43x + 67y = -24 ---(1)
67x + 43y = 24 ---(2)
There are different methods to find the solution, but one common approach is using the method of substitution. Here's how you can do it:
Step 1: Solve equation (1) for either x or y in terms of the other variable. Let's solve it for x:
43x + 67y = -24
Rearrange the equation:
43x = -67y - 24
Divide both sides by 43:
x = (-67y - 24) / 43
Step 2: Substitute the value of x in equation (2):
67x + 43y = 24
Replace x with the expression we found in step 1:
67[(-67y - 24) / 43] + 43y = 24
Step 3: Simplify and solve the resulting equation for y.
(-67*67y - 67*24) / 43 + 43y = 24
(-4489y - 1616)/43 + 43y = 24
Multiply the entire equation by 43 to remove the fraction:
-4489y - 1616 + 43*43y = 1032
Combine like terms:
-4489y + 1849y = 1032 + 1616
-2640y = 2648
Divide by -2640 to solve for y:
y = -2648 / -2640 = 1
Step 4: Substitute the value of y back into equation (1) to solve for x:
43x + 67(1) = -24
43x + 67 = -24
43x = -24 - 67
43x = -91
Divide by 43 to solve for x:
x = -91 / 43 = -2.12 (approx.)
So, the solution to the system of equations is x = -2.12 and y = 1.
43x+67y = -24
67x+43y = 24
add them up, and you have
110x + 110y = 0
so, y = -x
There is no unique solution.