systems elimination/substitution flashcard review

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 is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the first step in using the substitution method?

Back

Get either variable by itself.

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, meaning they have the same slope but different y-intercepts.

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 can you check your solution for a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane and identifying the point(s) where they intersect.

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.

Front

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

Back

Multiply the second equation by 3 to align the coefficients of y, then add the equations to eliminate y and solve for x.

Front

What is the solution to the system of equations 3x + 4y = 12 and 6x + 8y = 24?

Back

The solution is infinitely many solutions, as the second equation is a multiple of the first.