Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of equations graphically?

Back

By graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the first step in solving the system: 3x - 2y = 14 and 2x + 2y = 6?

Back

You can use either substitution or elimination; for elimination, you might multiply the second equation to align coefficients.

Front

What is the solution to the system: y = 2x - 11 and -3y = -6x - 15?

Back

No solution (the lines are parallel).

Front

What is the solution to the system: 8x + 4y = 12 and y = -2x + 3?

Back

Infinitely many solutions (the equations represent the same line).

Front

What are the values of x and y in the system: 4x - 2y = 7 and x + 2y = 3?

Back

x = 2, y = 1/2.