Flashcard 12.06.24 P6

Front

What is a solution to a system of equations?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If both equations are satisfied, the point is a solution.

Front

What does it mean if a system of equations is inconsistent?

Back

It means there is no solution; the lines represented by the equations do not intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What does it mean when two lines intersect at one point?

Back

It means the system of equations has exactly one solution.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection points of the lines representing the equations on a coordinate plane.

Front

What is the first step in solving the system 6x + y = -1 and y = -3x - 4 by substitution?

Back

Substitute -3x - 4 for y in the first equation.

Front

What is the result of adding the equations -9x - 4y = -20 and 5x + 4y = 4?

Back

The result is -4x = -16.