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3 years ago

Solve the system using substitution: y + 8x = 10 and 2y - 4x = 40

Mathematics

1 answer:

exis [7]3 years ago

4 0

Answer:

Hence x = -1 and y = 18

Step-by-step explanation:

Given the system of equations

y + 8x = 10... 1

2y - 4x = 40 ... 2

From 1; y = 10-8x

Substitute into 2;

2(10-8x) - 4x = 40

20 - 16x - 4x = 40

20 - 20x = 40

-20x = 40 - 20

-20x = 20

x = -1

Recall that y = 10-8x

y = 10 - 8(-1)

y = 10 + 8

y = 18

Hence x = -1 and y = 18

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If y is proportional to the sqaure root of x and y equal x when x equal 5,evaluate y when x eqaul 9.

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Answer:

$y = 3\, \sqrt{5}$ when $x = 9$ .

Step-by-step explanation:

The question states that $y$ is proportional to $\sqrt{x}$ . In other words, there is a constant $a$ ( $a \ne 0$ ) such that $y = a\, \sqrt{x}$ for all $x \ge 0$ .

The question also states that $y = x$ when $x = 5$ . Make use of this equality to find the value of $a$ .

Since $x = 5$ and $y = x$ , it must be true that $y = 5$ . Substitute $x = 5\!$ and $y = 5\!$ into the equation $y = a\, \sqrt{x}$ and solve for $a$ :

$5 = a\, \sqrt{5}$ .

$\begin{aligned}a &= \frac{5}{\sqrt{5}} \\ &= \sqrt{5}\end{aligned}$ .

Thus, $y = \sqrt{5}\, (\sqrt{x})$ for all $x \ge 0$ .

Substitute in the value $x = 9$ to find the corresponding value of $y$ :

$\begin{aligned} y &= \sqrt{5} \, (\sqrt{9}) \\ &= \sqrt{5} \times 3 \\ &= 3\, \sqrt{5}\end{aligned}$ .

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scZoUnD [109]

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Step-by-step explanation:

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