Unit 8: System Study Guide

Front

What can be said about the lines y = 3x and y = 3(x - 1) after graphing them?

Back

They are parallel.

Front

Solve by substitution: -7x + 2y = 3 and 7x + y = 12. What is the solution?

Back

(1, 5)

Front

Graph y = x - 1 and y = 3x + 1. How many times do the two graphs intersect?

Back

1

Front

Is (5, 3) a solution to the system x - y = 2 and 4x - 3y = 11?

Back

Yes

Front

What is the intersection of the lines y = -4x + 10 and 3x - 2y = 13?

Back

(3, -2)

Front

Define parallel lines in the context of graphing.

Back

Parallel lines are lines in a plane that never meet; they have the same slope.

Front

What does it mean for two lines to intersect at one point?

Back

It means the lines cross each other at exactly one location, indicating a unique solution to the system.

Front

Explain the substitution method in solving systems of equations.

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the significance of the solution (x, y) in a system of equations?

Back

The solution represents the point where the graphs of the equations intersect, indicating the values of x and y that satisfy both equations.

Front

What does it mean if two lines are perpendicular?

Back

Perpendicular lines intersect at a right angle (90 degrees) and have slopes that are negative reciprocals of each other.