Systems of equations and inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

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

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 all equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of inequalities?

Back

It is represented by shaded regions on a graph, indicating the area where the solutions lie.

Front

What does the symbol '≥' mean in inequalities?

Back

It means 'greater than or equal to'.

Front

What does the symbol '<' mean in inequalities?

Back

It means 'less than'.

Front

How do you solve a system of equations graphically?

Back

By plotting each equation on the same graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.