Systems of Equations- Graphing & Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

It means that the graphs of the equations intersect at exactly one point.

Front

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

Back

It means that the graphs of the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, so they intersect at every point on that line.

Front

How do you solve a system of equations by graphing?

Back

1. Graph each equation on the same coordinate plane. 2. Identify the point(s) where the lines intersect.

Front

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

Back

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

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

How do you find the x-intercept of an equation?

Back

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

Front

What is the solution to the system of equations y = 1/2x + 2 and y = -3x + 9?

Back

The solution is (2, 3).

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: 1. Same slope, different intercepts = no solution. 2. Same slope, same intercept = infinitely many solutions. 3. Different slopes = one solution.