Question

What is the solution of the system of equations below$y = 2x + 8$, $3\left( { - 2x + y} \right) = 12$

Answer 1

Hint: Here we will find the solution for the given pair of systems of linear equations. It is easy to find the value of $x$ and $y$ by substitution method.

Complete step-by-step answer:
The method of solving by substitution works by solving one of the equations(we choose which one) for one of the variables(we choose which one), and then plugging this back into the other equation, substituting for the chosen variable and solving for the other. Then we back solve for the first variable.
Here is how it works, given system of equations is
$y = 2x + 8$--------------- (1)
$3\left( { - 2x + y} \right) = 12$---------- (2)
The idea here is to solve one of the equations for one of the variables, and plug this into the other equation.
It does not matter which equation or which variable you pick. There is no right or wrong choice; the answer will be the same, regardless. But some choices may be better than others.
For instance, in this case, we can see that we can solve the second equation for $'x = '$ .
From equation (1) we can substitute $y = 2x + 8$ in equation (2) we get,
$ \Rightarrow 3\left( { - 2x + 2x + 8} \right) = 12$
$ \Rightarrow 3\left( 8 \right) = 12$
$ \Rightarrow 24 = 12$
It may be seen, $LHS \ne RHS$.
Hence there is inconsistency in the given statement and no solution.

Note: Keep in mind that, when solving, you are trying to find where the lines intersect. What if they don’t intersect? Then you are going to get some kind of wrong answer when you assume that there is a solution. That this system represents two parallel lines. But we tried to find the intersection point anyway. And we got a garbage result. Since there was not any intersection point.