Solving Systems of Equations

Front

What is a system of linear equations?

Back

A set of 2 or more equations that share the same variables.

Front

What is the elimination method in solving systems of equations?

Back

A technique where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

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

What is the first step in solving the system by elimination: 2x + 3y = 9 and 5x + 3y = 21?

Back

Multiply one equation by -1 to eliminate y.

Front

Solve the system using substitution: y = -6x + 5 and -2x + y = 5.

Back

(0, 5)

Front

What is the graphical representation of a solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.

Front

How can you check if your solution to a system of equations is correct?

Back

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