Solve by Substitution 6x+3y=24 , 4x+2y=-26

Problem

{[6*x+3*y=24],[4*x+2*y=−26])

Solution

1. Solve for one variable in the first equation. We can isolate y by subtracting 6*x from both sides and then dividing by 3

6*x+3*y=24

3*y=−6*x+24

y=−2*x+8

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

4*x+2*(−2*x+8)=−26

3. Distribute the constant into the parentheses.

4*x−4*x+16=−26

4. Combine like terms on the left side of the equation.

0*x+16=−26

16=−26

5. Analyze the result of the equation. Since 16 = -26$ is a false statement and all variables have been eliminated, the system of equations is inconsistent.

6. Conclude the solution based on the contradiction. This means the two lines are parallel and never intersect.

Final Answer

No solution

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