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

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the lines represented by the equations are the same line, so they intersect at every point on that line.

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

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

Front

What is the graphing method?

Back

The graphing method involves graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the first step in solving a system of equations?

Back

The first step is to write down the equations clearly and identify the variables.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check by substituting the solution back into the original equations to see if both equations are satisfied.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It has the form y = mx + b.

Front

What does 'm' represent in the equation of a line?

Back

In the equation y = mx + b, 'm' represents the slope of the line, indicating its steepness and direction.