Solve by Substitution 2x+4y=25 , x+5y=2

Problem

{[2*x+4*y=25],[x+5*y=2])

Solution

1. Isolate the variable x in the second equation by subtracting 5*y from both sides.

x=2−5*y

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

2*(2−5*y)+4*y=25

3. Distribute the 2 into the parentheses.

4−10*y+4*y=25

4. Combine the like terms involving y

4−6*y=25

5. Isolate the term with y by subtracting 4 from both sides.

−6*y=21

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

y=−21/6

7. Simplify the fraction by dividing the numerator and denominator by 3

y=−7/2

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

x=2−5*(−7/2)

9. Multiply the constants to find x

x=2+35/2

10. Find a common denominator to add the terms.

x=4/2+35/2

x=39/2

Final Answer

(x,y)=(39/2,−7/2)

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