Systems of equations review

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 infinitely many solutions?

Back

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

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you determine the solution of a system of equations graphically?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

What is the solution to the system: 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

If a system of equations has exactly one solution, what does this indicate about the lines?

Back

The lines intersect at exactly one point.

Front

What is the meaning of the term 'consistent' in relation to systems of equations?

Back

A consistent system has at least one solution.