Solving System of Equations by 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 solve a system of equations by graphing?

Back

It involves plotting the equations on a graph and finding the point(s) where they intersect.

Front

What is substitution in the context of solving equations?

Back

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

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

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

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

By identifying the intersection point(s) of the graphed lines.

Front

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

Back

Solve one of the equations for one variable in terms of the other variable.

Front

If y = 2x + 3, what is y when x = 1?

Back

y = 5.

Front

What is the graphical representation of the equation y = 4x - 2?

Back

A straight line with a slope of 4 and a y-intercept of -2.