To solve the given system by substitution, you solve the first equation for y and substitute into the second equation, which results in a contradiction, indicating the system has no solution.
To solve the system of equations 2x + y = -12 and -4x - 2y = 30 using substitution, follow these steps:
- Solve the first equation for y: y = -2x - 12.
- Substitute the expression for y into the second equation: -4x - 2(-2x - 12) = 30.
- Simplify the substituted equation: -4x + 4x + 24 = 30.
- Notice that the x terms cancel out, and you're left with 24 = 30, which is a contradiction.
Since there is a contradiction, the system has no solution and the lines represented by these equations are parallel.