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Andrews [41]
3 years ago
5

Solve, using the substitution method. 2x + 3y = 3 x + 2y = 1 (1, 4) (0, –2) (3, –1) (7, -5/2)

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
6 0

Answer:

x = 3 and y = -1

Step-by-step explanation:

using substitution method

let;

2x + 3y = 3 ................ equation 1

x + 2y = 1 ...................... equation 2

from equation 2

x + 2y = 1 ...................... equation 2

x = 1 - 2y .................... equation 3

substitute  for  x = 1 - 2y  in equation 1

2x + 3y = 3 ................ equation 1

2 ( 1 - 2y) + 3y = 3

Open the bracket  

2 -4y + 3y = 3

2 - y = 3

-y = 3 - 2

-y = 1

multiply both sides by -

therefore y = -1

put y = -1 in equation 3

x = 1 - 2y .................... equation 3

x = 1 - 2 ( -1)

x = 1 + 2

x = 3

therefore x = 3 and y = -1

to check for the correctness of your answer put the value of x = 3 and y = -1 in any of the equations. e.g

x = 1 - 2y .................... equation 3

3 = 1 - 2(-1)

3= 3................................. proved

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Which of the following expressions are equivalent to 7.2 ÷ -8.1 ÷ -3.7?
Inessa05 [86]

Step-by-step explanation:

7.2 / (-8.1) / (-3.7) = Positive

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3 0
3 years ago
You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta
vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x:  -\sqrt{2}   -\sqrt{2}  \sqrt{2}  \sqrt{2}

y:      -1         1     -1     1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }

m = -\frac{\cos 2\theta}{\sin \theta}

The tangent line is horizontal when m = 0. Then:

\cos 2\theta = 0

2\theta = \cos^{-1}0

\theta = \frac{1}{2}\cdot \cos^{-1} 0

\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right), for all i \in \mathbb{N}_{O}

\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}, for all i \in \mathbb{N}_{O}

The first four solutions are:

x:   \sqrt{2}   -\sqrt{2}  -\sqrt{2}  \sqrt{2}

y:     1        -1        1     -1

The solutions listed from the smallest to the greatest are:

x:  -\sqrt{2}   -\sqrt{2}  \sqrt{2}  \sqrt{2}

y:      -1         1     -1     1

6 0
2 years ago
The length of a rectangle is three times its breadth if the breadth is decreased by 2 m and breadth increased by 4 m the area of
White raven [17]

Answer:

Let the breadth is x, then the length is 3x.

<u>The area is:</u>

  • A = lw = 3x*x = 3x²

<u>The breadth is decreased by 2 m: </u>

  • w = x - 2

<u>The length is increased by 4m: </u>

  • l = 3x + 4

<u>The area is now:</u>

  • (x - 2)(3x + 4) = 3x² - 1/3(3x²)
  • 3x² +  4x - 6x - 8 = 2x²
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The breadth was 4 m and the length  12 m

8 0
2 years ago
4х – 9у – 2 = 0 <br>12х - 5у + 38 = 0 <br>answer in x and y intercept​
garri49 [273]

Answer:

x=5

y=2

Step-by-step explanation:

-3(4х – 9у – 2 = 0)

=-12x+27y+6

12х - 5у + 38    

-12x+27y+6

22y=44

y=2

x:

4x-9(2)-2=

=4x-20

4x=20

x=5

3 0
3 years ago
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