Alg. 2, Sect. 3-1 and 3-2 Flashcard Review

Front

What is the solution to the system of equations -2x + 4y = 16 and -x + 5y = 11?

Back

The solution is (-6, 1).

Front

How do you evaluate the expression (xy)(y^2) when x = 3 and y = 2?

Back

Substituting the values gives (3*2)(2^2) = 6*4 = 24.

Front

What is the ordered pair solution for the system of equations -2x - 8y = 2 and -3x - 10y = -1?

Back

The solution is (7, -2).

Front

How do you simplify the expression -10n + 9n?

Back

The simplified expression is -n.

Front

What is the solution to the system of equations y = x - 2 and y = 7x + 4 by graphing?

Back

The solution is (-1, -3).

Front

What is the method to solve a system of equations graphically?

Back

To solve graphically, plot both equations on the same graph and identify the point(s) where they intersect.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

Front

What is the difference between a dependent and an independent system of equations?

Back

A dependent system has infinitely many solutions (the lines are the same), while an independent system has exactly one solution (the lines intersect at one point).

Front

How can you determine if a system of equations is inconsistent?

Back

A system is inconsistent if the lines are parallel and do not intersect, meaning there are no solutions.

Front

What is the substitution method for solving systems of equations?

Back

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