Solve by Substitution x+y=85 , 0.25x+0.05y=11.25

Problem

{[x+y=85],[0.25*x+0.05*y=11.25])

Solution

1. Isolate a variable in the first equation. We can subtract y from both sides to solve for x

x=85−y

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

0.25*(85−y)+0.05*y=11.25

3. Distribute the 0.25 into the parentheses.

21.25−0.25*y+0.05*y=11.25

4. Combine the like terms containing y

21.25−0.20*y=11.25

5. Isolate the y term by subtracting 21.25 from both sides.

−0.20*y=−10

6. Solve for y by dividing both sides by −0.20

y=50

7. Substitute the value of y back into the expression for x to find the final value.

x=85−50

x=35

Final Answer

(x,y)=(35,50)

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