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3 years ago

-2(8+8x)+7x=-7x+2(x-8)

Mathematics

1 answer:

Inessa [10]3 years ago

7 0

x=0 .

−2(8+8x)+7x=−7x+2(x−8)

Step 1: Simplify both sides of the equation.

−2(8+8x)+7x=−7x+2(x−8)

(−2)(8)+(−2)(8x)+7x=−7x+(2)(x)+(2)(−8)(Distribute)

−16+−16x+7x=−7x+2x+−16

(−16x+7x)+(−16)=(−7x+2x)+(−16)(Combine Like Terms)

−9x+−16=−5x+−16

−9x−16=−5x−16

Step 2: Add 5x to both sides.

−9x−16+5x=−5x−16+5x

−4x−16=−16

Step 3: Add 16 to both sides.

−4x−16+16=−16+16

−4x=0

Step 4: Divide both sides by -4.

−4x /−4 = 0 /−4

x=0

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write the equation of a line that passes through the point (-3,-11) and is parallel to the line whose equation is 2x - y = 4

Vladimir79 [104]

Step-by-step explanation:

2x-y=4 means y=2x-4. -> slope of the parallel line is 2.

so using pt slope form,

y+11=2(x+3)

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3 years ago

3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em />

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First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

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<h3>Good luck with your studies.</h3>

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2 years ago

Solve the equations below. With explanations please.

Sophie [7]

Answer:

Step-by-step explanation:

y=-2x-4

y=5x+5

------------

-2x-4=5x+5

-2x-5x-4=5

-7x-4=5

-7x=5+4

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x=9/-7

x=-9/7

y=5(-9/7)+5

y=-45/7+35/7

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Answer: x=-9/7, y=-10/7. (-9/7, -10/7).

----------------------------------------------------

-3x+y=8

2y=6x-10

----------------

6x-2y=10

-3x+y=8

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y=8-(-3x)=8+3x

6x-2(8+3x)=10

6x-16-6x=10

-16=10

no solution

Answer: No Solution

--------------------------------

2y=4(x+3)

y-2x=6

--------------

y=4x+12

y=2x+6

--------------

4x+12=2x+6

4x-2x+12=6

2x+12=6

2x=6-12

2x=-6

x=-6/2

x=-3

y=2(-3)+6=-6+6=0

Answer: x=-3, y=0. (-3, 0).

-------------------------------------

x+2y=4

4x-2y=16

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x=20/5

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y=0

Answer: x=4, y=0. (4, 0).

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