Solve by Substitution 5x+6y=100 , 2x+3y=46

Problem

{[5*x+6*y=100],[2*x+3*y=46])

Solution

1. Isolate a variable in one of the equations. We will solve the second equation for y

2*x+3*y=46

3*y=46−2*x

y=(46−2*x)/3

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

5*x+6*((46−2*x)/3)=100

3. Simplify the equation by dividing 6 by 3

5*x+2*(46−2*x)=100

4. Distribute the constant and combine like terms to solve for x

5*x+92−4*x=100

x+92=100

x=8

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

y=(46−2*(8))/3

y=(46−16)/3

y=30/3

y=10

Final Answer

(x,y)=(8,10)

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