Systems 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 set of values that satisfy all equations in the system.

Front

How do you represent the sum of two numbers in an equation?

Back

If x and y are the two numbers, their sum can be represented as x + y = S, where S is the total sum.

Front

What does it mean for two numbers to have a difference?

Back

The difference between two numbers x and y is represented as x - y = D, where D is the difference.

Front

How can you express a relationship where one number is a certain amount younger than another?

Back

If x is the younger person's age and y is the older person's age, you can express this as x = y - A, where A is the age difference.

Front

What is the method to solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph. The point where the lines intersect represents the solution to the system.

Front

What is substitution in solving systems of equations?

Back

Substitution involves solving one equation for one 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

How do you set up a system of equations from a word problem?

Back

Identify the variables, translate the relationships and conditions into equations, and then write them as a system.

Front

What is a real-world example of a system of equations?

Back

A real-world example is calculating the total cost of items purchased, where the cost of each item and the quantity purchased are represented in equations.

Front

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

Back

A system has no solution if the equations represent parallel lines that never intersect.