Solving Linear Systems with Substitution & Graphing

Front

What is a linear equation?

Back

A linear equation is an equation that makes 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

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is substitution in solving linear systems?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the graphical method of solving linear systems?

Back

The graphical method involves graphing each equation on the same set of axes and identifying the point(s) where the lines intersect.

Front

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

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system.

Front

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

Back

If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

Front

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

Back

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

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.