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-intercept form of the equation 2y = 10x + 14?

Back

y = 5x + 7.

Front

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

Back

It means the system has no solution because the lines never intersect.

Front

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

Back

It means the system has infinite solutions because every point on the line is a solution.

Front

How do you find the solution to a system of equations graphically?

Back

By graphing both equations and identifying the point(s) where they intersect.

Front

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

Back

(3, 0).

Front

What is the solution to the system of equations y = 3x + 1 and y = 2x - 4?

Back

(5, 16).