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Svetradugi [14.3K]
2 years ago
12

Solve the system of equations x + y = 4 and -9x + 7y = -84 by combining the equations.

Mathematics
1 answer:
Yanka [14]2 years ago
6 0

Answer:

x = 7

y = -3

Step-by-step explanation:

x + y = 4                 (Multiply this by 9)

-9x + 7y = -84

9x + 9y = 36

-9x + 7y = -84

16y = -48

y = -3

x + y = 4  

x - 3 = 4

x = 7

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Give the equation of a line that goes through the point ( − 21 , 2 ) and is perpendicular to the line 7 x − 4 y = − 12 . Give yo
nlexa [21]

Given:

Equation of line 7x-4y=-12.

To find:

The equation of line  that goes through the point ( − 21 , 2 ) and is perpendicular to the given line.

Solution:

The given equation of line can be written as

7x-4y+12=0

Slope of line is

\text{Slope}=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}

m_1=-\dfrac{7}{(-4)}

m_1=\dfrac{7}{4}

Product of slopes of two perpendicular lines is -1. So, slope of perpendicular line is

m_1m_2=-1

m_2=-\dfrac{1}{m_1}

m_2=-\dfrac{4}{7}           [\because m_1=\dfrac{7}{4}]

Now, the slope of perpendicular line is m_2=\dfrac{4}{7} and it goes through (-21,2). So, the equation of line is

y-y_1=m_2(x-x_1)

y-2=-\dfrac{4}{7}(x-(-21))

y-2=-\dfrac{4}{7}x-\dfrac{4}{7}(21)

y-2=-\dfrac{4}{7}x-12

y=-\dfrac{4}{7}x-12+2

y=-\dfrac{4}{7}x-10

Therefore, the required equation in slope intercept form is y=-\dfrac{4}{7}x-10.

7 0
3 years ago
What multiples to 42 and adds to -2
solniwko [45]

Answer:

Step-by-step explanation:

xy = 42

x+y = - 2                   Substitute into the top equation

y = -2 - x                   Put in for y

x(-2 - x) = 42             Remove the brackets

-2x - x^2 = 42           Subtract 42 from both sides.

-2x - x^2 - 42 = 0      Put in the more normal order.

-x^2 - 2x - 42 = 0      Multiply by -1

x^2 + 2x + 42 = 0

This cannot be factored. It gives complex roots as it is written. I will give you the answer but I kind of doubt the question is correct.

x1 = - 1 + 6.40i

x2 = -1 - 6.40i

Leave a comment if you have a correction.

4 0
3 years ago
Change 6.00pm to 24 hours clock time<br><br>use a colon <br><br>​
kkurt [141]

Answer:

<h3>18:00 </h3>

Step-by-step explanation:

6:00 PM equals 18:00 in 24 hrs clock time.

<h3>Hope it helps you.. </h3>

3 0
2 years ago
Evaluating expressions for the value of x 4.5x-12 x=2
Svetradugi [14.3K]

X = 2

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9 -12

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Answer is -3

4 0
3 years ago
Simplify: 2/5y−4+7−9/10y
algol13
It’s a nightmare question
7 0
3 years ago
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