Solving Systems by Substitution [easy]

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: y = x - 5 and 2x + y = 10?

Back

Substitute y in the second equation: 2x + (x - 5) = 10.

Front

What is the solution to the system: y = x - 5 and 2x + y = 10?

Back

(5, 0)

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the solution to the system: y = 10 and y = 3x + 1?

Back

(3, 10)

Front

How do you determine if a system 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: x = 3 and y = 2x + 5?

Back

(3, 11)

Front

What does it mean for two lines to intersect?

Back

It means they have a common solution, which is the point of intersection.

Front

What is the solution to the system: 2x + 3y = 6 and y = 2?

Back

(0, 2)