How to Solve the System of Equations: x + 3y = 1 and 2x + 2y = 6

To solve the system of equations given by:

• Equation 1: x + 3y = 1
• Equation 2: 2x + 2y = 6

We can use the method of substitution or elimination. Here, I’ll demonstrate the elimination method.

First, let’s rearrange both equations for easier manipulation:

1. From Equation 1, we can express x in terms of y:
   • x = 1 – 3y
2. Now substitute this expression for x into Equation 2:

Substituting into Equation 2:

2(1 – 3y) + 2y = 6

Now, distribute the 2:

2 – 6y + 2y = 6

Combine like terms:

2 – 4y = 6

Next, isolate the variable y:

-4y = 6 – 2

-4y = 4

Now divide by -4:

y = -1

With y found, we can now substitute back to find x. Substitute y = -1 into the expression we found for x:

x = 1 – 3(-1)

x = 1 + 3

x = 4

So, the solution to the system of equations is:

• x = 4
• y = -1

This means the solution to the system of equations is (4, -1).