Solve the following system of equations.
x+y=13
22x+36y=356
22x + 22y = 286
Subtract that from 22x+36y=356
14 y = 70
y = 5
x = 8
To solve the system of equations, you can use the method of substitution or the method of elimination. I will demonstrate how to use the method of substitution.
Step 1: Solve one equation for one variable
Let's solve the first equation for x:
x + y = 13
Rearrange the equation:
x = 13 - y
Step 2: Plug the expression for x into the second equation
Now substitute the expression for x into the second equation:
22x + 36y = 356
Replace x with 13 - y:
22(13 - y) + 36y = 356
Step 3: Solve the equation for y
Expand the equation:
286 - 22y + 36y = 356
Combine like terms:
14y + 286 = 356
Now, isolate the variable by subtracting 286 from both sides:
14y = 356 - 286
14y = 70
Divide both sides by 14:
y = 70 / 14
y = 5
Step 4: Find the value of x
Now that we have found the value of y, plug it back into one of the original equations to solve for x. Let's use the first equation:
x + y = 13
Replace y with 5:
x + 5 = 13
Subtract 5 from both sides to isolate x:
x = 13 - 5
x = 8
Step 5: Check the solution
To ensure the solution is correct, substitute the values of x and y into both original equations:
Equation 1: x + y = 13
8 + 5 = 13 (True)
Equation 2: 22x + 36y = 356
22(8) + 36(5) = 356 (True)
Both equations are true when x = 8 and y = 5. Therefore, the solution to the system of equations is x = 8 and y = 5.