To solve the system of equations, we have:
- Equation 1: 2x + 3y = 40
- Equation 2: 2x + 2y = 20
We can use either substitution or elimination method. Here, we’ll use the elimination method for simplicity.
First, we notice that both equations have the term 2x, so we can eliminate x by subtracting Equation 2 from Equation 1:
(2x + 3y) – (2x + 2y) = 40 – 20
This simplifies to:
3y – 2y = 20
Which leads to:
y = 20
Now that we have the value of y, we can substitute it back into one of the original equations to find x. We’ll use Equation 2:
2x + 2(20) = 20
This simplifies to:
2x + 40 = 20
Subtracting 40 from both sides, we get:
2x = 20 – 40
Which simplifies to:
2x = -20
Dividing by 2 gives us:
x = -10
Thus, the solution for the system of equations is:
x = -10 and y = 20.
To summarize, we used the elimination method to find that the values of x and y satisfy both equations.