Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to intersect?

Back

It means they have a common solution, which is the point where they meet.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point where the graphs of the equations intersect.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if two lines are parallel?

Back

They have the same slope and will never intersect, indicating no solution.

Front

What does it mean if two lines are the same?

Back

They have infinite solutions because every point on the line is a solution.

Front

What is the first step in solving a system of equations by graphing?

Back

Graph both equations on the same coordinate plane.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, indicating the value of y when x=0.

Front

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

Back

Set y to 0 and solve for x.

Front

What is substitution in the context of solving systems of equations?

Back

Replacing one variable with an equivalent expression from another equation.