System 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 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 other variable.

Front

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

Back

Identify the variables and write the equations based on the information given in the problem.

Front

How do you represent the total number of coins in a word problem?

Back

You can represent the total number of coins with an equation like d + n = total, where d is the number of dimes and n is the number of nickels.

Front

What is the value of a dime in dollars?

Back

A dime is worth $0.10.

Front

What is the value of a nickel in dollars?

Back

A nickel is worth $0.05.

Front

If Dennis has 80 coins in total, how can you express this in an equation?

Back

You can express this as d + n = 80, where d is the number of dimes and n is the number of nickels.

Front

How do you set up an equation for the total value of coins?

Back

You can set it up as 0.10d + 0.05n = total value in dollars.

Front

What is the solution to the system of equations: x + y = 55 and x - y = 3?

Back

The solution is (29, 26), where x is Mr. Micklow's age and y is Ms. Craft's age.

Front

What does it mean if two equations are consistent?

Back

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