Solve by Substitution 4x+3y=85 , 3x+5y=115

Problem

{[4*x+3*y=85],[3*x+5*y=115])

Solution

1. Isolate one variable in the first equation. We will solve for y in terms of x

4*x+3*y=85

3*y=85−4*x

y=(85−4*x)/3

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

3*x+5*((85−4*x)/3)=115

3. Multiply the entire equation by 3 to clear the fraction.

9*x+5*(85−4*x)=345

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

9*x+425−20*x=345

−11*x+425=345

−11*x=−80

x=80/11

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

y=(85−4*(80/11))/3

y=(85−320/11)/3

y=(935−320)/11/3

y=615/11/3

y=205/11

Final Answer

(x,y)=(80/11,205/11)

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