Solving Systems 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 the context of solving equations?

Back

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

Front

How do you solve for y in the equation y = 3 - x?

Back

To find y, substitute any value of x into the equation.

Front

What is the first step in solving the system: y = 8x + 1 and y = 6x + 3?

Back

Set the two equations equal to each other: 8x + 1 = 6x + 3.

Front

What is the solution to the system: x = -3y - 17 and 2x + 3y = -7?

Back

(10, -9)

Front

What is the solution to the system: y = x + 5 and 4x + y = 20?

Back

(3, 8)

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 = 3 - x and 3y + x = 5?

Back

(2, 1)

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if they hold true.