Solve Systems of Equations by Substitution

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 substitution in the context of solving equations?

Back

Replacing one variable with an expression involving another variable.

Front

How do you determine if a system of equations has one solution, no solution, or infinite solutions?

Back

By analyzing the graphs of the equations: one solution means they intersect at one point, no solution means they are parallel, and infinite solutions mean they are the same line.

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

If y = 2x + 1, what is y when x = 1?

Back

y = 3.

Front

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

Back

It means that the values of x and y at that point satisfy both equations.

Front

What is the solution to the system of equations y = 4x - 1 and y = 2x + 1?

Back

(1, 3).

Front

If you have the equations y = -4x + 4 and y = 8, what is the solution?

Back

(-1, 8).

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.