Solving Systems by Graphing: Key Concepts and Techniques

What is a system of equations?

• A set of unrelated equations

• A single equation with multiple variables

• Two or more equations with the same variables

• An equation with no variables

Graphically, what represents the solution to a system of equations?

• The y-intercept of the lines

• The slope of the lines

• The point where the lines intersect

• The distance between the lines

What type of solution do parallel lines represent?

• Infinitely many solutions

• No solution

• One solution

• Two solutions

What does it mean when two lines are coincident?

• They intersect at one point

• They are parallel

• They are the same line

• They never intersect

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

• Solve for one variable

• Rewrite the equations in slope-intercept form

• Find the y-intercept

• Find the x-intercept

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

• x = my + b

• y = ax^2 + bx + c

• ax + by = c

• y = mx + b

In the example y = x - 8, what is the slope (m) and y-intercept (b)?

• m = -1, b = 8

• m = 8, b = -1

• m = 1, b = -8

• m = -8, b = 1

What is the point of intersection for the lines y = x - 8 and y = -2x + 1?

• (3, -5)

• (5, -3)

• (1, -3)

• (3, 5)

What type of line does the equation y = 7 represent?

• Vertical line

• Diagonal line

• Horizontal line

• No line

If two lines have the same slope but different y-intercepts, what can be concluded?

• They intersect at one point

• They are parallel and have no solution

• They are the same line

• They have infinitely many solutions