linear systems - substitution method

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

How do you convert an equation to slope-intercept form?

Back

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

Front

What is the slope of a line?

Back

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

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

How do you find the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, found by setting x = 0 in the equation.

Front

What is the solution to the system of equations y = 2/3x - 2 and y = -x + 3?

Back

The solution is (3, 0).

Front

What is the solution to the system of equations 2y = 10x + 14?

Back

The equation in slope-intercept form is y = 5x + 7.