FRIDAY MAY 3RD : Identifying Solutions to 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 for a system of equations to have a unique solution?

Back

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

Front

What are the possible types of solutions for a system of equations?

Back

1. One solution (intersecting lines) 2. No solution (parallel lines) 3. Infinitely many solutions (coincident lines)

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What does it mean if two lines intersect at a point?

Back

The coordinates of the intersection point are the solution to the system of equations.

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

How can you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the intersection point.

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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.