Systems of Equations and Inequalities

Front

What is a system of equations with infinitely many solutions?

Back

A system of equations with infinitely many solutions will have lines that are the same.

Front

What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point.

Front

What is the solution to the system of equations 3x + 7y = 23 and -3x - 7y = -17?

Back

No solution.

Front

How do you solve the system by substitution: y = -6x + 5 and -2x + y = 5?

Back

The solution is (0, 5).

Front

What is the solution to the system of equations 4x + 9y = 28 and -4x - y = -28?

Back

The solution is (7, 0).

Front

What is the graphical representation of a system of equations with no solution?

Back

The lines are parallel and never touch.

Front

What does it mean if two lines in a system of equations are coincident?

Back

It means they are the same line, resulting in infinitely many solutions.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for a variable and substituting that expression into the other equation.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function.