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3 years ago

What is the solution of the system of equations?

Mathematics

1 answer:

umka21 [38]3 years ago

7 0

No solution of the system of equations y = -2x + 5 and -5y = 10x + 20 ⇒ 2nd answer

Step-by-step explanation:

Let us revise the types of solutions of a system of linear equations

One solution
No solution when the coefficients of x and y in the two equations are equal and the numerical terms are different
Infinitely many solutions when the coefficients of x , y and the numerical terms are equal in the two equations

∵ y = -2x + 5

- Add 2x to both sides

∴ 2x + y = 5 ⇒ (1)

∵ -5y = 10x + 20

- Subtract 10x from both sides

∴ -10x - 5y = 20

- Divide both sides by -5

∴ 2x + y = -4 ⇒ (2)

∵ The coefficient of x in equation (1) is 2

∵ The coefficient of x in equation (2) is 2

∴ The coefficients of x in the two equations are equal

∵ The coefficient of y in equation (1) is 1

∵ The coefficient of y in equation (2) is 1

∴ The coefficients of y in the two equations are equal

∵ The numerical term in equation (1) is 5

∵ The numerical term in equation (2) is -4

∴ The numerical terms are different

From the 2nd rule above

∴ No solution of the system of equations

No solution of the system of equations y = -2x + 5 and -5y = 10x + 20

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

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False Any three points are always coplanar

False Two points are always collinear

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Read explanations, as the answer to these questions, is subjective.

Step-by-step explanation:

The definition of coplanar is; figures that exist on the same plane. Any three points might not always be colinear, as some points might exist on one plane, but other points could exist on other planes. To visualize this phenomenon, refer to the attached image. Two points could be on the red plane, but the third could be on the green. Therefore, while there are three points, not all of them exist on the same plane. However, another plane can be constructed to connect these points, bear in mind certain problems might specifically indicate that three points are not coplanar, therefore, the answer is false.

The definition of collinear is existing on the same line. This statement is a little subject, it can be both true and false depending on the way one looks at it. A line can be drawn to connect any two points, one only needs two points to determine a line. So technically two points are always collinear. However, it also depends on the circumstance. Certain geometry problems might specifically indicate that two points are not collinear. Thus, it really depends on the context. Therefore, the answer is technically false.

Two planes usually intersect on a line. To understand this, please refer to the image attached. Tehcnailly, if a corner of one plane intersects another, then one can state that the plane intersects on a point, but typically, planes intersect on lines. Therefore, technically the answer to this problem is false, as two planes usually intersect on a line.

Images credits: Geogebra