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

Problem

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

Solution

1. Solve the first equation for y in terms of x

3*x+2*y=8

2*y=8−3*x

y=4−3/2*x

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

2*x+3*(4−3/2*x)=7

3. Distribute the constant and simplify the equation.

2*x+12−9/2*x=7

4/2*x−9/2*x=7−12

−5/2*x=−5

4. Solve for x by multiplying both sides by the reciprocal.

x=−5⋅(−2/5)

x=2

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

y=4−3/2*(2)

y=4−3

y=1

Final Answer

(x,y)=(2,1)

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