Solving Systems of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

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

Front

What is the solution to a system of equations represented graphically?

Back

The point(s) where the lines intersect.

Front

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

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect.

Front

What is the substitution method for solving systems of equations?

Back

Solving one equation for a variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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.