Final answer:
The system of equations y=2x+4 and 6x-3y=30 has no solution because after substitution and simplification, we get an inconsistent equation, which implies the lines are parallel.
Step-by-step explanation:
To solve the system by substitution with the given equations y=2x+4 and 6x−3y=30, we first substitute y from the first equation into the second equation, and then find the value of x.Step-by-Step Explanation:First, we identify the known equation, y=2x+4. Then, we substitute y into the second equation, 6x-3y=30, which becomes 6x-3(2x+4)=30. We simplify this to obtain 6x-6x-12=30, which further simplifies to -12=30, indicating an inconsistency. This means there is no solution because the lines represented by these equations are parallel and do not intersect.
To solve the system of equations by substitution, we need to solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation. Let's solve the first equation for y:y = 2x + 4Now substitute this expression for y in the second equation:6x - 3(2x + 4) = 30Simplify and solve for x:6x - 6x - 12 = 30-12 = 30The equation is inconsistent, which means there is no solution to the system of equations.