Solve by Substitution 3x-3y=1 , 12x+9y=11

Problem

{[3*x−3*y=1],[12*x+9*y=11])

Solution

1. Solve the first equation for x by adding 3*y to both sides and dividing by 3

3*x=1+3*y

x=(1+3*y)/3

x=1/3+y

2. Substitute the expression for x into the second equation.

12*(1/3+y)+9*y=11

3. Distribute the 12 through the parentheses.

4+12*y+9*y=11

4. Combine like terms and solve for y

4+21*y=11

21*y=7

y=7/21

y=1/3

5. Substitute the value of y back into the expression for x

x=1/3+1/3

x=2/3

Final Answer

(x,y)=(2/3,1/3)

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