Solving systems by elimination

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and 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, so every point on the line is a solution.

Front

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point, the system has one solution.

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

What is the first step in solving the system by elimination?

Back

Identify which variable can be eliminated by adding or subtracting the equations.

Front

Solve the system: x + 4y = -3 and x + 7y = -12.

Back

(9, 3)

Front

What is the next step after aligning the equations for elimination?

Back

Multiply one of the equations by a number to make the coefficients of one variable equal.

Front

Solve by elimination: 2x + 3y = 9 and 5x + 3y = 21.

Back

Multiply the first equation by -1 to eliminate y.

Front

What is the solution to the system: x + 6y = 17 and x - 3y = 8?

Back

(11, 1)