SYSTEM OF EQUATIONS elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does the elimination method involve?

Back

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

Front

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

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Front

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

Back

It means that the equations represent the same line, and there are an infinite number of points that satisfy both equations.

Front

Solve the system of equations: 5x - 3y = -36 and 2x + 3y = 15.

Back

(-3, 7)

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Solve the system of equations: -2x - 10y = 22 and 2x + 5y = -12.

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(-1, -2)

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

How can you make the coefficients of a variable the same in both equations?

Back

You can multiply one or both equations by a number to achieve the same coefficient for the variable you want to eliminate.

Front

Solve the system of equations: 3x + 4y = 12 and 6x - 2y = 18.

Back

(2, 0)

Front

What is the solution to the system of equations: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinitely Many Solutions