M7D3 Solving Linear Systems Using Substitution

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a system of equations by substitution?

Back

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

Front

What is the solution of a system of equations?

Back

The solution is the point where the equations intersect, representing the values of the variables that satisfy all equations in the system.

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you determine if two lines are intersecting?

Back

Two lines are intersecting if their slopes are different, meaning they will cross at one point.

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other.

Front

If y = 2x + 3, what is y when x = 2?

Back

y = 2(2) + 3 = 7.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the rise over run.