Solve by Substitution 0.05x+0.25y=22 , 0.15x+0.05y=24

Problem

{[0.05*x+0.25*y=22],[0.15*x+0.05*y=24])

Solution

1. Clear the decimals by multiplying both equations by 100 to make the coefficients integers.

5*x+25*y=2200

15*x+5*y=2400

2. Simplify the first equation by dividing every term by 5

x+5*y=440

3. Isolate x in the simplified first equation to prepare for substitution.

x=440−5*y

4. Substitute the expression for x into the second integer equation (15*x+5*y=2400.

15*(440−5*y)+5*y=2400

5. Distribute and combine like terms to solve for y

6600−75*y+5*y=2400

−70*y=2400−6600

−70*y=−4200

y=60

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

x=440−5*(60)

x=440−300

x=140

Final Answer

(x,y)=(140,60)

Want more problems? Check here!