Solve by Substitution 12x+15y=240 , 10x+25y=300

Problem

{[12*x+15*y=240],[10*x+25*y=300])

Solution

1. Simplify the second equation by dividing every term by 5 to make it easier to isolate a variable.

2*x+5*y=60

2. Isolate the variable x in the simplified second equation.

2*x=60−5*y

x=30−2.5*y

3. Substitute the expression for x into the first original equation, 12*x+15*y=240

12*(30−2.5*y)+15*y=240

4. Distribute the 12 into the parentheses.

360−30*y+15*y=240

5. Combine like terms and solve for y

360−15*y=240

−15*y=−120

y=8

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

x=30−2.5*(8)

x=30−20

x=10

Final Answer

(x,y)=(10,8)

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