The ordered pair (-2,4) satisfies the system if it makes a true statement in both equations. Let's substitute x=-2 and y=4 into each of the equations and simplify.
One of our resulting statements, 4=-4, is not true. Thus, the point (-2,4) does not satisfy the system of equations.
b
We want to know if the ordered pair (-2,4) satisfies the following system of equations.
{y=-x+2y=3x+10
We can investigate that by substituting x=-2 and y=4 into both equations and simplifying the resulting equation. The ordered pair satisfies the system only if both equations then are true.
Since both statements are true the point (-4,-2) is contained in the solution set of the system.
c
We have been asked to determine if the ordered pair (-2,4) is a solution to the following system of equations.
{-6x+3y=-24-4x−4y=-24
Let's find out by substituting x=-2 and y=4 into both equations. If both equations are true the ordered pair is a solution.