Solve by Substitution x+3y=15 , 4x+y=6

Problem

{[x+3*y=15],[4*x+y=6])

Solution

1. Isolate a variable in one of the equations. We can solve the first equation for x by subtracting 3*y from both sides.

x=15−3*y

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

4*(15−3*y)+y=6

3. Distribute the constant into the parentheses.

60−12*y+y=6

4. Combine like terms to simplify the equation.

60−11*y=6

5. Solve for y by subtracting 60 from both sides and then dividing by −11

−11*y=−54

y=54/11

6. Substitute the value of y back into the expression for x found in step 1.

x=15−3*(54/11)

7. Simplify the expression to find the value of x

x=165/11−162/11

x=3/11

Final Answer

(x,y)=(3/11,54/11)

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