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2 years ago

Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 times

Mathematics

1 answer:

Kryger [21]2 years ago

8 0

Answer:

8 and - 2

Step-by-step explanation:

let x be the larger number and y the smaller , then

x = 5y + 18 → (1)

3x + 4y = 16 → (2)

substitute x = 5y + 18 into (2)

3(5y + 18) + 4y = 16 ← distribute parenthesis and simplify left side

15y + 54 + 4y = 16

19y + 54 = 16 ( subtract 54 from both sides )

19y = - 38 ( divide both sides by - 19 )

y = - 2

substitute y = - 2 into (1)

x = 5(- 2) + 18 = - 10 + 18 = 8

then larger number is 8 and smaller is - 2

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If | 8x -2 | < 4, Which of the following is true of x? Explain as well.

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The true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75

<h3>What are inequality expressions?</h3>

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

<h3>How to determine the true expression of the variable x?</h3>

The inequality expression is given as

|8x - 2| < 4

Divide through the above equations by 2

So, we have the following inequality expression

|4x - 1| < 2

Remove the absolute value sign from the inequality expression

So, we have

-2 < 4x - 1 < 2

Add 1 to all sides of the above inequality expression

So, we have

-1 < 4x < 3

Divide through the above inequality expression by 4

So, we have

-0.25 < x < 0.75

Hence, the true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75

Write and solve a system of linear​ equations: The larger of two numbers is 18 more than 5 times

Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 times