SOLVING SYSTEMS OF EQUATIONS BY ELIMINATION

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

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 if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

Front

What does it mean if two lines are parallel in the context of systems of equations?

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, resulting in no points of intersection and thus no solutions.

Front

How can you solve the system of equations 2x + 9y = -7 and 6x - 3y = 9 using elimination?

Back

Multiply the first equation by 3 to align the coefficients of x, then subtract the second equation from the modified first equation to solve for y, and substitute back to find x.

Front

What is the solution to the system of equations 5x + 8y = -12 and 3x + 5y = -7 using elimination?

Back

The solution is (-4, 1).

Front

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

Back

It indicates that the equations represent parallel lines that do not intersect.

Front

What is the first step in using the elimination method?

Back

The first step is to manipulate the equations to align the coefficients of one variable so that it can be eliminated.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the values of the solution back into the original equations to see if they satisfy both equations.

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.