5.1-5.3 Solve Systems of Equations - Graphing & Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by graphing?

Back

To solve a system of equations by graphing means to plot each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine the number of solutions in a system of equations?

Back

A system can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

What is the significance of the point (3, -7) in the context of a system of equations?

Back

The point (3, -7) is the solution to the system of equations, meaning it satisfies both equations.

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other.

Front

What does the equation d + c = 50 represent in the context of the farm problem?

Back

It represents the total number of donkeys (d) and chickens (c) on the farm, which adds up to 50.

Front

What does the equation 4d + 2c = 174 represent in the context of the farm problem?

Back

It represents the total number of legs from the donkeys and chickens, where donkeys have 4 legs and chickens have 2 legs.

Front

What does it mean if a system of equations has 0 solutions?

Back

It means the lines represented by the equations are parallel and will never intersect.

Front

What is the graphical representation of the solution to the system y = -3x - 4 and y = -8x - 9?

Back

The solution is the point (-1, -1), where the two lines intersect on the graph.