Solve by substituting method 3x + 4y = 10, 2x - 2y = 2.

To solve the system of equations using the substitution method, we have the following equations:

Equations

• 1. 3x + 4y = 10
• 2. 2x - 2y = 2

Step 1: Solve one equation for a variable

Let's solve the second equation for x:

2x - 2y = 2

Divide everything by 2:

x - y = 1

Now, isolate x:

x = y + 1

Step 2: Substitute into the first equation

Now, substitute x in the first equation:

3(y + 1) + 4y = 10

Distribute:

3y + 3 + 4y = 10

Combine like terms:

7y + 3 = 10

Step 3: Solve for y

Subtract 3 from both sides:

7y = 7

Now, divide by 7:

y = 1

Step 4: Find x using the value of y

Substitute y back into the equation for x:

x = 1 + 1

x = 2

Final Solution

The solution to the system of equations is:

• x = 2
• y = 1