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 set them equal to the given totals.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the solution to a system of equations?

Back

The solution is the point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane and identify 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

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

Back

It means the lines are parallel and never intersect, indicating that there are no values for the variables that satisfy both equations.