Systems Elimination & 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 to solve a system of equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

How do you represent the cost of items in a system of equations?

Back

You can represent the cost of items as variables. For example, let x = cost of a hotdog and y = cost of a soda.

Front

If Bailey bought 2 hotdogs and 1 soda for $5.50, how can this be expressed in an equation?

Back

Front

If Chloe bought 1 hotdog and 2 sodas for $5.00, how can this be expressed in an equation?

Back

Front

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

Back

The first step is to write the equations in a standard form, aligning like terms.

Front

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

Back

If two lines are parallel, it means there is no solution to the system, as the lines never intersect.

Front

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

Back

If two lines coincide, it means there are infinitely many solutions, as they are the same line.

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 they hold true.

Front

Back

The solution is (-2, 5).