Elimination - Without Common Coefficients

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique for solving systems of linear equations by eliminating one variable, allowing for the solution of the remaining variable.

Front

What does it mean to have 'no common coefficients' in elimination?

Back

'No common coefficients' means that the coefficients of the variables in the equations do not share a common factor, which may require manipulation of the equations to align coefficients for elimination.

Front

Solve for x: 2x + 3y = 12 and 4x - y = 5.

Back

x = 2.

Front

Solve for y: 2x + 3y = 12 and 4x - y = 5.

Back

y = 2.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations to align the coefficients of one variable for elimination.

Front

How do you eliminate a variable in a system of equations?

Back

You can eliminate a variable by adding or subtracting the equations after adjusting their coefficients to be equal.

Front

What is the solution to the system: x + 2y = 8 and 3x - y = 7?

Back

(3, 1.5).

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the point(s) where the equations intersect, indicating the values of the variables that satisfy all equations simultaneously.

Front

What happens if the system of equations has no solution?

Back

If there is no solution, the lines represented by the equations are parallel and do not 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 every point on that line is a solution.