Eschool - Systems of Equations using 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 when a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean when a system of equations has infinite 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

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

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

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

Back

Isolate one variable in one of the equations.

Front

If y = 2x + 9 and x = -3, what is the value of y?

Back

y = 3.

Front

What is the solution to the system of equations: 2x + 3y = 12 and x - y = 3?

Back

(6, 3).

Front

What does the equation 4 = 7 signify in terms of solutions?

Back

It signifies that there is no solution, as the statement is false.

Front

What is the significance of the equation 2 = 2 in a system of equations?

Back

It indicates that there are infinite solutions, as it is always true.