Solve Systems by Inspection

Front

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

Back

Solving by inspection means finding the solution to a system of equations by looking for values that satisfy both equations without performing algebraic manipulations.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

No solution means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

One solution means that the lines represented by the equations intersect at exactly one point.

Front

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

Back

Infinitely many solutions mean that the equations represent the same line, so every point on the line is a solution.

Front

Given the equations y = ¾x + 5 and y = -¾x + 5, how many solutions does this system have?

Back

One Solution.

Front

Given the equations y = ¾x + 5 and y = ¾x + 2, how many solutions does this system have?

Back

No Solution.

Front

What is the solution to the system of equations y = x - 2 and y = -x + 1?

Back

(1, -1).

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

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.