System of Equations - Study Guide

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

How do you solve a system of equations by graphing?

Back

To solve by graphing, plot each equation on the same graph and identify the point(s) where they intersect.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the slope-intercept form of a line?

Back

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

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

Front

What does it mean if two lines are coincident?

Back

If two lines are coincident, they lie on top of each other and have infinitely many solutions.

Front

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

Back

You can determine the number of solutions by analyzing the slopes and y-intercepts of the lines: one solution (intersecting), no solution (parallel), or infinitely many solutions (coincident).

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

How do you find the intersection point of two lines algebraically?

Back

To find the intersection point algebraically, solve the system of equations simultaneously using substitution or elimination.

Front

What is the elimination method?

Back

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