Solve 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

How do you determine which variable to eliminate in a system of equations?

Back

Look for coefficients that can easily be made equal or opposite through multiplication, allowing for straightforward elimination when the equations are added or subtracted.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

No solution (the equations are dependent, representing the same line).

Front

Solve by elimination: 5x - 2y = 3 and 3x + 4y = 11. What is the solution?

Back

(2, 1).

Front

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

Back

It means 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 the equations represent the same line, and there are countless points of intersection.

Front

Solve by elimination: 3x + 4y = 10 and 6x + 8y = 20. What is the solution?

Back

Infinitely many solutions (the second equation is a multiple of the first).

Front

How can you check your solution after solving a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

Solve by elimination: 8x - 2y = 14 and 4x + y = 10. What is the solution?

Back

(2, 0).

Front

What is the first step in using the elimination method?

Back

Align the equations and decide which variable to eliminate.