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 a unique solution?

Back

It means that the equations intersect at exactly one point.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so they intersect at every point on that line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the substitution method for solving systems of equations?

Back

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

Front

What is the elimination method for solving systems of equations?

Back

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

Front

Solve for x and y: x - 2y = 1 and x + 4y = 7.

Back

(1, 1) - The solution is x=1, y=1.

Front

Solve for x and y: y = 2x + 1 and y = 4x - 1.

Back

(1, 3) - The solution is x=1, y=3.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.