# Solve x – 2y = 6. 3x – 6y = 18. . A. (2, –2). B. (3, negative three halves) C. No Solutions D. Infinitely Many Solutions

Answer: It would be helpful if we write the equations given above in the slope-intercept form which is expressed as:

y = mx + b

We do as follows:

x – 2y = 6
y = x/2 - 3

3x – 6y = 18
y = x/2 - 3

By looking at the equations, we can see that the two equations are the same. Thus, the correct answer is option D. There are infinitely many solutions.

The equations has infinitely many solutions. Option (D) is correct.

Further explanation:

Consider and

If then the system of equation has exactly one solution and the system of equations are consistent.

If then the system of equation has infinite many solution and the system of equations are consistent.

If then the system of equation has no solution and the system of equations are inconsistent.

Given:

The options are as follows,

A.

B.

C. No Solutions

D. Infinitely Many Solutions

Explanation:

The equations are

The ratio of can be calculated as follows,

The system of equations has infinite many solutions.

The equations has infinitely many solutions. Option (D) is correct.

Subject: Mathematics

Chapter: Linear equation

Keywords: consistent, inconsistent, equations, system of equations, parallel lines, intersecting lines, coincident lines, no solution, many solutions, one solution.

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Ten times anumber increased by four is no more than twenty-five

The mathematical expression is;

⇒ 10x + 4 < 25

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''ten times a number increased by four is no more than twenty-five''

Now,

Let a number = x

So, We can formulate;

The mathematical expression is;

⇒ 10x + 4 < 25

Thus, The mathematical expression is;

⇒ 10x + 4 < 25