22 - 23 Flashcard - Substitution / Elimination

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

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

Solve using substitution: y = 2x + 3, x + y = 10

Back

(2, 6)

Front

Solve using elimination: 3x + 2y = 12, 4x - 2y = 8

Back

(2, 3)

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system when substituted into them.

Front

Is the point (3, 1) a solution to the system: x + y = 4, 2x - y = 5?

Back

No

Front

Solve the system using elimination: 5x + 3y = 9, 2x - y = 4

Back

(3, -1)

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions.

Front

Solve using substitution: y = x + 1, 2y - x = 4

Back

(3, 4)