System of Equations Test - Honors

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 if a system of equations has no solution?

Back

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

Front

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

Back

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

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

By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinitely many solutions.

Front

Solve the system using substitution: 2x + 3y = 6 and y = x - 2. What is the solution?

Back

(3, -1)

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane, where the solution(s) are the intersection points.

Front

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

Back

It means that the system of equations has exactly one solution.

Front

What is the solution to the system of equations: 3x + 4y = 12 and 6x + 8y = 24?

Back

Infinitely Many Solutions (the second equation is a multiple of the first).

Front

What is the first step in using the substitution method?

Back

Isolate one variable in one of the equations.