Systems and 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 problem into equations based on the relationships described, and set them equal to each other.

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

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

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, where m is the slope and b is the y-intercept.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the intersection of two lines graphically?

Back

Graph both equations on the same coordinate plane. The point where they intersect is the solution to the system.

Front

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

Back

If two lines are parallel, they have no points of intersection, meaning the system has no solution.

Front

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

Back

If two lines coincide, they are the same line, meaning there are infinitely many solutions.