4.2 Systems - Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the points where the graphs of the equations intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

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

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

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

Back

(1, 3)

Front

What is the solution to the system: y = x - 2 and -2x + 3y = -1?

Back

(5, 3)

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means the system has no solutions, as the lines never intersect.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at exactly one point.

Front

What is the solution to the system: y = 6x - 11 and -2x - 3y = -7?

Back

(2, 1)

Front

What is the solution to the system: 3y - 2x = 0 and y = 4x - 1?

Back

(0.3, 0.2)

Front

What is substitution in the context of solving equations?

Back

Replacing one variable with an expression involving another variable to simplify the system.