Solving systems of equations by substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression derived from another equation.

Front

Solve the system of equations: y = 8x + 1 and y = 6x + 3.

Back

(1, 9)

Front

What indicates infinite solutions in a system of equations?

Back

When the equations represent the same line.

Front

Solve the system of equations: y = 2x + 3 and y = -x + 1.

Back

(1, 5)

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

Solve the system of equations: 2x + 3y = 6 and x - y = 1.

Back

(3, 0)

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

Solve the system of equations: 3x + 4y = 12 and 6x + 8y = 24.

Back

Infinite solutions.