Is (-4, -2) a solution to the following system of equations? x + y = -6 14x + 20y = 16

Understand the Problem

The question asks whether the point (-4, -2) is a solution to the given system of linear equations. To determine this, we need to substitute x = -4 and y = -2 into both equations and check if the equations hold true.

Answer

No

Steps to Solve

Substitute $x = -4$ and $y = -2$ into the first equation

Substitute the given values into $x + y = -6$: $$ -4 + (-2) = -6 $$ Simplify: $$ -6 = -6 $$ The first equation is satisfied.

Substitute $x = -4$ and $y = -2$ into the second equation

Substitute the given values into $14x + 20y = 16$: $$ 14(-4) + 20(-2) = 16 $$ Simplify: $$ -56 - 40 = 16 $$ $$ -96 = 16 $$ The second equation is not satisfied.

Check if the point is a solution to the system

Since the point $(-4, -2)$ satisfies the first equation but not the second equation, it is not a solution to the system of equations. A solution to a system of equations must satisfy all equations in the system.

More Information

A point is a solution to a system of equations if it satisfies all equations in the system. In this case, the point (-4, -2) satisfies the first equation but not the second, so it is not a solution to the system.

Tips

A common mistake is to only check one of the equations. A point must satisfy all equations in the system to be a solution.

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