Solving 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 no solution?

Back

If the equations represent parallel lines, they do not intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

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

Given the equations y = 2x + 1 and y = 4x - 1, what is the solution?

Back

(1, 3)

Front

Given the equations y = -6x + 5 and -2x + y = 5, what is the solution?

Back

(0, 5)

Front

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

Back

There is a unique solution to the system of equations.

Front

Given the equations y = -2x + 5 and y = 2x - 11, what is the solution?

Back

(4, -3)