Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

What is the first step in solving the system: 3x + 2y = 16 and 7x + y = 19?

Back

You can use either substitution or elimination to start solving the system.

Front

What does the solution (2,5) represent in a system of equations?

Back

It represents the values of x and y that satisfy both equations in the system.

Front

What is the meaning of the inequality y ≤ 3x?

Back

It means that the value of y is less than or equal to three times the value of x.

Front

How can you represent a real-world problem as a system of equations?

Back

Identify the variables, write equations based on the relationships, and ensure they reflect the problem's constraints.