To solve the system of equations 2x + 3y = 40 and 2x + 2y = 20, we can use either the substitution method or the elimination method. Here, we’ll use the elimination method for clarity.
First, we can align the two equations for clarity:
- Equation 1: 2x + 3y = 40
- Equation 2: 2x + 2y = 20
Next, we can eliminate one variable. Since both equations have the same coefficient for 2x, we can subtract Equation 2 from Equation 1:
(2x + 3y) – (2x + 2y) = 40 – 20
This simplification results in:
3y – 2y = 20
y = 20
Now that we have the value of y, we can substitute this back into one of the original equations to solve for x. We can use Equation 2:
2x + 2(20) = 20
This simplifies to:
2x + 40 = 20
Now, subtract 40 from both sides:
2x = 20 – 40
2x = -20
Dividing by 2 gives:
x = -10
Thus, the solution to the system of equations is:
- x = -10
- y = 20
In conclusion, the solution to the system of equations 2x + 3y = 40 and 2x + 2y = 20 is (x, y) = (-10, 20).