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2 years ago

X+2y=5 and 4x-12y=-20 solve using elimination and substitution

Mathematics

1 answer:

mixer [17]2 years ago

5 0

Answer:

(1,2)

Step-by-step explanation:

Substitution:

x + 2y = 5 Solve for x

x = -2y + 5 Substitute -2y + 5 in for x in the second equation

4x - 12y = -20

4(-2y + 5) - 12y = -20 Distribute the 4

-8y + 20 - 12 y = -20 Combine the y term

-20y + 20 = -20 Subtract 20 from both sides

-20y = -40 Divide both sides by -20

y = 2

Plug y into either of the 2 original equations to get x.

x + 2y = 5

x + 2(2) = 5

x + 4 = 5

x = 1

The answer is (2,1).

Elimination:

x + 2y = 5 4x - 12y = -20. We want to eliminate with the x or the y. I am going to eliminate the x's that means that I have to multiply the first equation all the way through by -4

(-4)(x + 2y) = (5) (-4) That makes the equivalent expression

-4x - 8y = -20 I will add that to 4x - 12y = -20

4x - 12y = -20

0x -20y = -40

-20y = -40

y = 2. Plug 2 into either the 2 original equation to find x. This time I will select the second original equation to find x.

4x -12y = -20

4x - 12(2) = -20

4x - 24 = -20

4x = 4

x = 1

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lara31 [8.8K]

Answer:

'The closest distance between Earth and Jupiter is greater than the closest distance between Earth and Mercury by approximately 7.66 times'.

Step-by-step explanation:

We are given that,

Distance between Earth and Jupiter = 5.9 × 10⁸ kilometers

Distance between Earth and Mercury = 7.7 × 10⁷ = 0.77 × 10⁸ kilometers

So, we see that,

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Also, Ratio = $\frac{5.9\times 10^8}{0.77\times 10^8} =7.66$

That is,

'The closest distance between Earth and Jupiter is greater than the closest distance between Earth and Mercury by approximately 7.66 times'.

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3 years ago

Show work please \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$