x+y=20
x=y-4
Please help me solve each system of equations and show your work thanks
use substitution, sub the 2nd into the 1st
x+y = 20
(y-4) + y = 20
2y = 24
y = 12
back into x = y-4
x = 12-4 = 8
x = 8, y = 12
To solve this system of equations, we can use the method of substitution. Let's solve it step by step:
Step 1: Solve one equation for one variable in terms of the other variable.
From equation 2, we have:
x = y - 4
Step 2: Substitute the expression of the variable from step 1 into the other equation.
Substitute x = y - 4 into equation 1:
(y - 4) + y = 20
Step 3: Simplify and solve for the remaining variable.
Combine like terms:
2y - 4 = 20
Add 4 to both sides of the equation:
2y = 24
Divide both sides by 2:
y = 12
Step 4: Substitute the value of y back into one of the original equations to find the value of the other variable.
Substitute y = 12 into equation 2:
x = 12 - 4
x = 8
Step 5: Check your solution by substituting the values of x and y into the other equation.
Substitute x = 8 and y = 12 into equation 1:
8 + 12 = 20
Both sides of the equation are equal, so the solution (x = 8, y = 12) is correct.
Therefore, the solution to the system of equations is x = 8 and y = 12.