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4 years ago

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If equation one is mutiplied by 2 and then the equations are added the result is 2x+y=3 X-2y=-1

1 answer:

zloy xaker [14]4 years ago

8 0

Question:

2x + y = 3, x - 2y = –1.

If equation one is multiplied by 2 and then the equations are added, the result is _____.

(A) 3x = 2

(B) 3x = 5

(C) 5x = 5

Answer:

Option C:

5x = 5

Solution:

Given equations are

2x + y = 3 – – – – (1)

x – 2y = –1 – – – – (2)

Let us first multiply equation (1) by 2, we get

(1) × 2 ⇒ 4x + 2y = 6 – – – – (3)

Now, add equation (3) to equation (2).

⇒ x – 2y + 4x + 2y = –1 + 6

Combine like terms together.

⇒ x + 4x – 2y + 2y = –1 + 6

⇒ 5x = 5

So, if equation one is multiplied by 2 and then the equations are added, the result is 5x = 5.

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Determine whether LINE AB and LINE CD are parallel, perpendicular, or neither. A(−1, −4) , B(2, 11) , C(1, 1) , D(4, 10) ( write

Luba_88 [7]

Step-by-step explanation:

Hey there!

The points of line AB are; (-1,-4) and (2,11).

Note:

Use double point formula and simplify it to get two eqaution.
Use condition of parallel lines, perpendicular lines to know whether the lines are parallel or perpendicular or nothing.

~ Use double point formula.

$(y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)$

~ Keep all values.

$(y + 4) = \frac{11 + 4}{2 + 1} (x + 1)$

~ Simplify it.

$y + 4 = \frac{15}{3} (x + 1)$

$y + 4 = 5x + 5$

$5x - y + 1 = 0$

Therefore this is the equation of line AB.

Now, Finding the equation of line CD.

Given;

The points of line CD are; (1,1) and (4,10).

~ Using formula.

$(y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1)$

~ Keep all values.

$(y - 1) = \frac{10 - 1}{4 - 1} (x - 1)$

~ Simplify it.

$y - 1 = 3 x - 3$

$3x - y - 2 = 0$

Therefore, 3x - y- 2 = 0 is the eqaution of line CD.

Use condition of parallel lines.

m1= m2

Slope of equation (i)

$m1 = \frac{ - coeff. \: of \: x}{coeff \: of \: y}$

$m1 = \frac{ - 5}{ - 1}$

Therefore, m1 = 5

Slope of second equation.

$m2 = \frac{ - coeff \: .of \: x}{coeff \: .of \: y}$

$m2 = \frac{ - 3}{ - 1}$

Therefore, m2 = 3.

Now, m1≠m2.

So, the lies are not parallel.

Check for perpendicular.

m1*m2= -1

3*5≠-1.

Therefore, they aren't perpendicular too.

So, they are neither.

<em><u>Hope </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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N76 [4]

Answer:

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Step-by-step explanation:

Hello There!

If you didn't know opposite angles are congruent in parallelograms

So ∠A≅∠C and ∠B≅∠D

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Answer:

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Step-by-step explanation:

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