Substitution Basics

Front

What is a solution to a system of equations?

Back

A point \( (x,y) \) where the equations intersect.

Front

How should the solution \( y=9 \) and \( x=-2 \) be written?

Back

\( (-2,9) \)

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

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

Back

The lines are parallel and never intersect.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one equation for one variable.

Front

What is the substitution method?

Back

A method where you solve one equation for a variable and substitute that expression into the other equation.

Front

If \( x = -3 \), what do you need to find next?

Back

You need to find the value of \( y \).

Front

What is the general form of a linear equation?

Back

\( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.

Front

What is the significance of the slope in a linear equation?

Back

It represents the rate of change of \( y \) with respect to \( x \).