Systems of Equations- Graphing & Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to graph a system of equations?

Back

It means to plot the equations on a coordinate plane and find the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you find the y-coordinate of the solution in a system of equations?

Back

By determining the point of intersection of the two equations on a graph.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

How do you solve the system: y = 4x + 1 and 3x + 2y = 13?

Back

Substitute y from the first equation into the second to find x, then back-substitute to find y.

Front

What is the graphical representation of the equation y = 8x + 1?

Back

A straight line with a slope of 8 and a y-intercept of 1.

Front

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

Back

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