Solving Systems of Equations

Front

What is the solution (x, y) to a system of equations?

Back

The point where the equations intersect.

Front

How do you solve a system of equations by substitution?

Back

Replace one variable with an expression from another equation.

Front

What is the solve-intercept form of an equation?

Back

An equation written as y = mx + b, where m is the slope and b is the y-intercept.

Front

Solve the system of equations: 9x - 4y = 1 and -3x + 8y = -47.

Back

(-3, -7)

Front

What does 'a' represent in the ticket sales problem?

Back

The number of adult tickets sold.

Front

What does 'c' represent in the ticket sales problem?

Back

The number of children's tickets sold.

Front

Write the system of equations for the ticket sales problem: Homer sold 21 tickets for a total of $104.

Back

a + c = 21 and 6a + 4c = 104.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a graph, where the solution is the intersection point.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and eliminate one variable by adding or subtracting.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.