Practice with Elimination add/subtract

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

How do you solve a system of equations using elimination?

Back

To solve a system of equations using elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

Front

What is a zero pair in the context of elimination?

Back

A zero pair is a pair of numbers that add up to zero, which allows for the elimination of a variable when solving equations.

Front

What does it mean if a system of equations has one solution?

Back

If a system of equations has one solution, it means that the two lines represented by the equations intersect at exactly one point.

Front

What is the first step in solving the system 4x + 8y = 20 and -4x + 2y = -30 using elimination?

Back

The first step is to align the equations and decide which variable to eliminate by adding or subtracting the equations.

Front

What do you need to multiply an equation by to create a zero pair?

Back

You need to multiply the equation by a number that will make the coefficients of one of the variables equal and opposite in the two equations.

Front

What is the solution to the system 7x + 2y = 24 and 8x + 2y = 30?

Back

The solution to the system is (6, -9).

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

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

Back

If a system of equations has infinitely many solutions, it means that the equations represent the same line, and every point on that line is a solution.