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6. which of the following system does not have the real solution?

a. x + y = 2
4x + 4y = 8
b. 3x - 2y = 4
3x - 2y =10
c. 3x - 2y = 4
6x - 4y = 8
d. 5x + 2y = 2
15x + 6y = 6

7. Graph the system:
3x + 5y = 5
6x + 10y = 10
a. Two coinciding line
b. Two distinct parallel lines
c. Two horizontal lines
d. Two lines intersecting at one point

8. Two lines in a system of linear equation in two variable coincide. How solutions does this system have?
a. Infinite solution
b. No real solutions
c. One distinct solution
d. Two solution

9. Which of these following method is used to find a system of linear equation in two variables?
a. Elimination method
b. Graphical method
c. Substitution method
d. All of the above

10. Which of the following system has exactly one real solution?
a. 5x + 2y = 2
2x - 5y = 2
b. 5x + 2y = 2
10x + 4y = 4
c. 5x + 2y = 4
15x + 6y = 12
d. 5x + 2y = 8
5x + 2y = 6​

User Kevin Pei
by
5.9k points

1 Answer

5 votes

Answer:

See below

Explanation:

6. a. x + y = 2

4x + 4y = 8

If we rewrite both in standard slope-intercept format, we will see the issue:

y = -x + 2

4y = -4x + 8

y = -x + 2

These equations are the same. There are an infinite number of solutions. All points intersect. So it does not have a real solution. [Perhaps it has a real doozy of a solution.]

b. 3x - 2y = 4

3x - 2y =10

Rewrite both:

-2y = -3x + 4

y = (3/2)x - 2

---

-2y = -3x + 10

y = (3/2)x - 5

These equations are different, but they have the same slope, (3/2). They are parallel and thus will never intersect. There is no real solution.

c. 3x - 2y = 4

6x - 4y = 8

Rewrite both:

-2y = -3x + 4

y = (3/2)x -2

--

-4y = -6x + 8

y = (3/2)x + 8

Same slope of (3/2). Same answer for parallel lines.

d. 5x + 2y = 2

15x + 6y = 6

Rewrite both:

2y = -15x + 6

y = -(15/2)x + 2

---

6y = -15x + 6

y = -(15/6)x + 1

y = -(5/2)x + 1

These lines have different slopes, so they will intersect. This system has a real solution.

=

7. See attached graph for 7.

It's a surprise to find only one line. But rewrite the equations in standard format to reveal why there is only one line:

3x + 5y = 5

5y = -3x + 5

y = -(3/5)x + 1

---

6x + 10y = 10

10y = -6x + 10

y = -(6/10)x + 1

y = -(3/5)x + 1

These equations are the same: Two coinciding lines, to put it mildly.

8. I interpret "Two lines in a system of linear equation in two variable coincide" as both equations are the same. If that is a correct interpretation, Infinite solutions.

9. All three can be used.

10.

a. 5x + 2y = 2

2x - 5y = 2

One solution

They have different slopes. The first is -(5/2) and the second is (2/5). They are actually perpendicular to each other.

b. 5x + 2y = 2

10x + 4y = 4

Rewrite the 2nd equation by dividing by 2: 5x + 2y = 2

These equations are identical. They have an infinite number of solutions (more than 1)

c. 5x + 2y = 4

15x + 6y = 12

Rewrite the second equation:

d. 5x + 2y = 8

5x + 2y = 6​

These equations are identical. They have an infinite number of solutions (more than 1)

6. which of the following system does not have the real solution? a. x + y = 2 4x-example-1
User Royo
by
6.4k points
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