Flashcard #12 - Algebra 3

Front

Solve the system by substitution: x + y = 10, 2x - y = 3

Back

(4, 6)

Front

Define substitution method in solving systems of equations.

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

Solve for x: 3x + 5 = 20

Back

x = 5

Front

Homer sells tickets for admission to your school play. If adult tickets are $6 and children tickets are $4, and he sold 21 tickets for a total of $104, write the system of equations.

Back

x + y = 21, 6x + 4y = 104

Front

A 100-foot cable is cut into two pieces. The first piece is 18 feet longer than the second. Write the system of equations to find the lengths of each piece.

Back

x + y = 100, x = y + 18

Front

Solve the system of equations: x + y + z = 4, x = -2y, z = -3y

Back

(2, -1, 3)

Front

What is the graphical interpretation of a system of equations with no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

Explain the concept of dependent and independent variables in a system of equations.

Back

Independent variables can be freely changed, while dependent variables depend on the values of independent variables.

Front

Solve for y: 2y - 3 = 7

Back

y = 5

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.