Systems of Equations

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

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot the equations on a coordinate plane and identify the point(s) where the lines intersect.

Front

What does it mean for an ordered pair to satisfy a system of equations?

Back

An ordered pair satisfies a system of equations if it makes all the equations in the system true when substituted for the variables.

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 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 significance of the point (2, -4) in the context of systems of equations?

Back

The point (2, -4) is the solution to the system of equations y = x - 6 and y = -3x + 2, meaning it satisfies both equations.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and set up the system based on the problem's context.

Front

What is the value of a quarter in cents?

Back

A quarter is worth 25 cents.

Front

If a boy has seven more nickels than quarters and the total value is $4.90, how can you express this as a system of equations?

Back

Let q be the number of quarters and n be the number of nickels. The system is: n = q + 7 and 0.05n + 0.25q = 4.90.

Front

What is the first step in solving the system of equations 3x + 2y = 315 and 2x + 4y = 450?

Back

The first step is to choose a method (substitution or elimination) to solve for one variable.