Solve by Substitution x+2y=1 , 4x+5y=13

Problem

{[x+2*y=1],[4*x+5*y=13])

Solution

1. Isolate the variable x in the first equation by subtracting 2*y from both sides.

x=1−2*y

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

4*(1−2*y)+5*y=13

3. Distribute the 4 into the terms inside the parentheses.

4−8*y+5*y=13

4. Combine the like terms involving y

4−3*y=13

5. Solve for y by subtracting 4 from both sides and then dividing by −3

−3*y=9

y=−3

6. Substitute the value of y back into the isolated equation for x to find its value.

x=1−2*(−3)

x=1+6

x=7

Final Answer

(x,y)=(7,−3)

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