Substitution and Elimination flashcard

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

How do you solve the system x + y = 19 and y = 3x - 1 using substitution?

Back

1. Substitute y in the first equation: x + (3x - 1) = 19. 2. Solve for x: 4x - 1 = 19 -> 4x = 20 -> x = 5. 3. Substitute x back to find y: y = 3(5) - 1 = 14. Solution: (5, 14).

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 solve the system 3x + y = 19 and 2x - y = 6 using elimination?

Back

1. Add the two equations: (3x + y) + (2x - y) = 19 + 6. 2. This simplifies to 5x = 25 -> x = 5. 3. Substitute x back to find y: 3(5) + y = 19 -> y = 4. Solution: (5, 4).

Front

What is the best method to solve the system 2x + 2y = 11 and 3x - 4y = -2?

Back

The best method is elimination because it allows for quick elimination of variables.

Front

How do you solve the system y = 7x + 9 and 2y + 2x = -18 using substitution?

Back

1. Substitute y in the second equation: 2(7x + 9) + 2x = -18. 2. Simplify: 14x + 18 + 2x = -18 -> 16x = -36 -> x = -2. 3. Substitute x back to find y: y = 7(-2) + 9 = -5. Solution: (-2, -5).

Front

What does it mean to 'eliminate' a variable in a system of equations?

Back

To 'eliminate' a variable means to manipulate the equations so that one variable cancels out, allowing for the other variable to be solved.

Front

What is the solution to the system y = -6 and -3x - 6y = 24?

Back

1. Substitute y: -3x - 6(-6) = 24 -> -3x + 36 = 24. 2. Solve for x: -3x = -12 -> x = 4. Solution: (4, -6).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

What is the graphical interpretation of a solution to a system of equations?

Back

The solution is the point where the graphs of the equations intersect.