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 solve a system of equations graphically?

Back

To solve a system of equations graphically, plot each equation on the same graph. The point(s) where the lines intersect represent the solution(s) to the system.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

Define the substitution method for solving systems of equations.

Back

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

Front

Define the elimination method for solving systems of equations.

Back

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

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What is the importance of defining variables in word problems?

Back

Defining variables helps clarify what each symbol represents, making it easier to translate the problem into mathematical equations.

Front

How do you check the solution of a system of equations?

Back

To check the solution, substitute the values back into the original equations to see if they satisfy all equations in the system.