Number of Solutions for Systems of Linear Equations, Solutions of Equations

no

Given a system of two linear equations, if the lines are parallel, there is ____ solution.

infinitely

Given a system of two linear equations, if the lines are coinciding (over-lapping), there are ___________ many solutions.

one

Given a system of two linear equations, if the lines have different slopes, there is ____ solution.

different

Parallel lines have the same slope but _____________ y-intercepts.

same

Coinciding lines have the same slope and the ________ y-intercept.

one

Consider the following system of linear equations.

I. 2x - y = 8

II. 4x + 6y = 13

How many solutions are there?

(one / none / infinitely many)

infinitely many

Consider the following system of linear equations.

I. 2x - 3y + 4 = 0

II. 4x - 6y + 8 = 0

How many solutions are there?

(one / none / infinitely many)

none

Consider the following system of linear equations.

I. 6y = 12 - x

II. x + 6y - 20 = 0

How many solutions are there?

(one / none / infinitely many)

TRUE

Two lines, each with a different slope, can have the same y-intercept.

TRUE or FALSE

one

Consider the following system of linear equations.

I. x = 5

II. y = 2

How many solutions are there?

(one / none / infinitely many)

infinitely many

Consider the following system of linear equations.

I. y - 7 = 6

II. y - 8 = 5

How many solutions are there?

(one / none / infinitely many)

none

Consider the following system of linear equations.

I. x = 4

II. x + 5 = 0

How many solutions are there?

(one / none / infinitely many)

24

Consider the following system of linear equations.

I. 2x + 5y = 12

II. 4x + 10y = C

For what value of C does the system have infinitely many solutions?

10

Consider the following system of linear equations.

I. 2x + 5y - 12 = 0

II. 4x + Cy - 9 = 0

For what value of C does the system have no solution?

one

Suppose two investments earn the same rate of interest. Which one of the following is not a possible number of solutions for the linear system representing the investments over time?

(one / none / infinitely many)

infinitely many

How many solutions are there to the following equation.

3x - 7y = 15

(one / none / infinitely many)

2x - x + 7 = x + 3 + 4

Infinitely many solutions

-2(x + 1) = -2x + 5

no solution

x + 2x + 7 = 3x - 7

no solution

4x + 2x + 2 = 3x - 7

x = -3

2x + 8 = 2(x + 4)

Infinitely many solutions

3(x - 1) = 2x + 9

x = 12

x + 2x + 7 = 3x - 7

no solution

10 + x = 5 (.2x + 2)

Infinitely many solutions

4(2x + 1) = 5x + 3x + 9

no solution

8(x + 2) = 2x + 16

x = 0

4x + 1 = 2(2x + 3)

no solution

4(x + 3) - 4 = 8(.5x + 1)

Infinitely many solutions

3x + 1 = 3(x - 1) + 4

Infinitely many solutions

5(x + 2) - 3x = 2(x + 5)

Ims

x + 5x + 4 = 3(2x - 1)

no solution

4x + 2x - 5 = 7x - 1

x = -4

2(3x + 3) = 3(2x + 2)

Infinitely many solutions

6(x + 1) + 5 = 13 - 2 + 6x

Infinitely Many solutions

3x + 7x + 1 = 2(5x + 1)

no solution

4(x + 1) = 4(2 - x)

x = 1/2