Systems of Equations Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure they reflect the problem's constraints.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

Front

What is the difference between independent and dependent systems of equations?

Back

Independent systems have exactly one solution (intersecting lines), while dependent systems have infinitely many solutions (coincident lines).

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

How can 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 substitution in solving systems of equations?

Back

Substitution involves solving one equation for a variable and then substituting that expression into the other equation.

Front

What is elimination in solving systems of equations?

Back

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

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.