Solve by Substitution 5x+3y=4 , 5x+y=9

Problem

{[5*x+3*y=4],[5*x+y=9])

Solution

1. Isolate a variable in one of the equations. We can solve the second equation for y by subtracting 5*x from both sides.

y=9−5*x

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

5*x+3*(9−5*x)=4

3. Distribute the constant into the parentheses.

5*x+27−15*x=4

4. Combine like terms to simplify the equation.

−10*x+27=4

5. Solve for x by subtracting 27 from both sides and then dividing by −10

−10*x=−23

x=23/10

6. Substitute the value of x back into the expression for y to find the second coordinate.

y=9−5*(23/10)

y=9−23/2

y=18/2−23/2

y=−5/2

Final Answer

(x,y)=(23/10,−5/2)

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