Linear equations (two variables)

a situation where there is no solution that satisfies all of the equations in the system; this happens when lines are parallel

• one solution

• consistent system

• inconsistent system

• infinite solutions

Is there a solution to the system of equations?

y = 4x + 3

y = 4x - 2

• No- because the lines will be parallel and will never intersect.

• No- because the lines have different y-intercepts

• Yes- because the lines will NOT be parallel

• Yes- because the lines have the same slope.

When both variables are eliminated resulting in a false statement, the system has no solution.

• True

• False

the system of equations do not intersect at any point resulting in parallel lines; there are no values that satisfy the system of equations; the lines will have the same slope but different y-intercepts

• Solution of a System

• X-Intercept

• No Solutions

• Graphing Method

-3x + 3y = 4

-x + y = 3

If two lines NEVER intersect, how many solutions will the system have?

• Infinitely Many Solutions

• One Solution

• Two Solutions

• No Solution

Which value of m will create a system of parallel lines with no solution?

y = mx -6

8x - 4y = 12

• $-2$

• $-\frac{1}{2}$

• $\frac{1}{2}$

• $2$

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Solve each system by elimination.

12x + 16y = 16

-12x - 16y = -16

• all real #'s

• no solution

What is the solution for a linear system that contains parallel lines?

• One solution

• No solution

• Infinitely Many solutions