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 by substitution?

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the first step in solving the system: 3x + y = 1 and y = 4x + 1?

Back

Substitute 4x + 1 for y in the first equation.

Front

What is the solution to the system: 3x + y = 1 and y = 4x + 1?

Back

(0, 1)

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at a single point.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression from another equation.

Front

What is the solution to the system: 7x + y = -20 and y = 3x + 10?

Back

(-3, 1)