Solve by Substitution 3x-2y=14 , 5x+4y=5

Problem

{[3*x−2*y=14],[5*x+4*y=5])

Solution

1. Solve the first equation for y to prepare for substitution.

3*x−2*y=14

−2*y=14−3*x

y=(3*x−14)/2

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

5*x+4*((3*x−14)/2)=5

3. Simplify the equation by distributing the constant.

5*x+2*(3*x−14)=5

5*x+6*x−28=5

4. Combine like terms and solve for x

11*x−28=5

11*x=33

x=3

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

y=(3*(3)−14)/2

y=(9−14)/2

y=−5/2

Final Answer

(x,y)=(3,−2.5)

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