Algebra 2 lesson 3.5Solving Systems of Equations

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 to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the graphical interpretation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

Solve the system by substitution: 5x + 4y = -14, y = -7x - 15.

Back

(-2, -1)

Front

Solve the system by substitution: x = -3y - 8, x - 2y = -3.

Back

(-5, -1)

Front

Solve the system using elimination: 2x + 3y = 5, 4x - y = 11.

Back

(3, 1)