Unit 3 Test Redemption #2

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

Front

What does it mean if a system of linear equations has one solution?

Back

It means that the two lines represented by the equations intersect at exactly one point.

Front

What does it mean if a system of linear equations has no solution?

Back

It means that the two lines are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

It means that the two lines are the same line, overlapping each other.

Front

How do you solve a system of equations by graphing?

Back

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

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 y-intercept of the equation y = 1/2x + 2?

Back

The y-intercept is 2, which is the point where the line crosses the y-axis.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines: if they are the same, there are infinitely many solutions; if they are parallel, there is no solution; if they intersect, there is one solution.

Front

What is the graphical representation of the equation y = -3x + 9?

Back

A straight line with a slope of -3 and a y-intercept of 9.

Front

What does it mean for two lines to be intersecting?

Back

It means that the lines cross at one point, indicating a unique solution to the system.