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 systems of equations?

Back

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

Front

Given the equations y = 6x - 11 and -2x - 3y = -7, what is the first step to solve for x using substitution?

Back

Substitute y from the first equation into the second equation.

Front

If y = 6x - 11, what is y when x = 2?

Back

y = 6(2) - 11 = 1.

Front

What is the solution to the system y = 6x - 11 and -2x - 3y = -7?

Back

(2, 1).

Front

What does the solution (4, 3) represent in a system of equations?

Back

It represents the point where the two lines intersect, indicating one solution.

Front

What is a 'One Solution' system?

Back

A system where the graphs of the equations intersect at exactly one point.

Front

What does a system with 'No Solution' look like on a graph?

Back

The lines are parallel and never intersect.

Front

What does a system with 'Infinite Solutions' look like on a graph?

Back

The lines are coincident, meaning they lie on top of each other.