12/10 Writing Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

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

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.

Front

What is the meaning of the solution (1, -1) in a system of equations?

Back

The solution (1, -1) means that when x = 1 and y = -1, both equations in the system are satisfied.

Front

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

Back

Substitute the solution values into both equations. If both equations are true, the solution is correct.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they have no solutions in common.