M7D3 Solving Linear Systems Using Substitution

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 does it mean if two lines intersect at one point?

Back

If two lines intersect at one point, it means the system of equations has one unique solution.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating the system has no solution.

Front

What does it mean if two lines are the same line?

Back

If two lines are the same line, it means they have infinitely many solutions, as every point on the line is a solution.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How can you check if your solution to a system of equations is correct?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

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.