System of Equations (Set Equal)

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 to set equations equal to each other?

Back

It means to find the point(s) where the graphs of the equations intersect by equating their expressions.

Front

How do you solve a system of equations by substitution?

Back

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

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

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

Back

It means there are infinite solutions, as every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

It means there is exactly one solution to the system, which is the point of intersection.

Front

Solve the system: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

Solve the system: 3x + y = -21 and x + y = -5.

Back

(-8, 3)