Solve by Substitution 2x+3y=7 , 3x+2y=8

Problem

{[2*x+3*y=7],[3*x+2*y=8])

Solution

1. Solve the first equation for x by subtracting 3*y from both sides and dividing by 2

2*x=7−3*y

x=(7−3*y)/2

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

3*((7−3*y)/2)+2*y=8

3. Clear the fraction by multiplying the entire equation by 2

3*(7−3*y)+4*y=16

4. Distribute the 3 and combine like terms to solve for y

21−9*y+4*y=16

21−5*y=16

−5*y=−5

y=1

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

x=(7−3*(1))/2

x=4/2

x=2

Final Answer

(x,y)=(2,1)

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