`-2x + 4y = -14` `3x + y = 21` Check whether the ordered pair (5,6) is a solution of the system.
Equation b, , can be rewritten as y = 21 - 3x. We can then substitute this into equation a. This results in the following equation:
-2x + 4(21-3x) = -14
The next step is to multiply out in the second term. This leaves us with:
-2x + 84 - 12x = -14
If we collect the like terms on the left side of the equation, and subtract 84 from both sides, we are left with:
-14x = -98
The next step is to divide both sides by -14. This tells us that
x = (-98/-14) = 7.
If x = 7, and y = 21 - 3x, then y = 0. ----> the solution is (7,0). (In other words, (5,6) is not a solution.)
A second, and perhaps simpler, way to prove this would be to simply plug (5,6) into the original two equations. The left side of equation b, then would be:
3(5) + 6 = 21 , which equals the right side of the equation.
Because the left side equals the right side, it is still possible that (5,6) might be a solution.
But before we can conclude anything, we must also check if (5,6) works as a solution to equation a. Plugging in, we find that the left side of equation a becomes
-2(5) + 4(6) = -10 + 24 =14
(and the right side is still -14.) Because 14 and -14 are NOT equal, (5,6) does not work as a solution to this set of equations.