Solve by Substitution 3x+3y=32400 , 4x+2y=54000

Problem

{[3*x+3*y=32400],[4*x+2*y=54000])

Solution

1. Simplify the first equation by dividing every term by 3 to isolate a variable more easily.

x+y=10800

2. Isolate the variable y in the simplified equation.

y=10800−x

3. Substitute the expression for y into the second original equation.

4*x+2*(10800−x)=54000

4. Distribute the constant 2 into the parentheses.

4*x+21600−2*x=54000

5. Combine like terms on the left side of the equation.

2*x+21600=54000

6. Subtract 21600 from both sides to isolate the term with x

2*x=32400

7. Divide by 2 to find the value of x

x=16200

8. Substitute the value of x back into the expression for y found in step 2.

y=10800−16200

9. Calculate the final value for y

y=−5400

Final Answer

(x,y)=(16200,−5400)

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