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3 years ago

A student solved a system of equations by elimination. Describe and correct the error made in the part of the solution shown.

Mathematics

1 answer:

ivanzaharov [21]3 years ago

7 0

Answer:

x = -2; y = 3

Step-by-step explanation:

5x + 4y = 2 (1)

3x + 3y = 3 (2)

Multiply (1) by 3 and (2) by 4

15x + 12y = 6 (3)

12x + 12y = 12 (4)

Subtract (4) from (3)

15x - 12x = 6 - 12

3x = -6

x = -6/3

x = -2

Substitute x = -2 into (1)

5x + 4y = 2

5(-2) + 4y = 2

-10 + 4y = 2

4y = 2 +10

4y = 12

y = 12/4

y = 3

The first error is when he multiplied equation (2) by 4

He didn't multiply the right hand side of the equation by 4

3x + 3y = 3 ×4

12x + 12y = 12

But he wrote

12x + 12y = 3

The the next error is subtracting the left hand side of the equation and adding the right hand side

15x + 12y = 6

12x + 12y = 3

He wrote

3x = 9

Instead of 3x = 3

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Please help!! Will mark first answerer brainiest!! Thank you so much!

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3 years ago

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If 6m by 15m is a pond ,is 40m would be enough for fencing the pond

Veseljchak [2.6K]

If the pond were a rectangle, then:
length=15 m
width=6 m

We would have to calculate the perimeter of this rectangle.
Perimeter of a rectangle=2(length)+2(width)

Perimeter of this rectangle=2(15 m)+2(6 m)=30 m+12 m=42 m

We need 42 m and I only have 40 m, therefore, it would not be enough for fencing the pond.

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3 years ago

In ΔABC, m∠A = 90° and AN is an altitude. If AB = 20 in and AC = 15 in, find BC, BN, NC, AN.

uranmaximum [27]

Since ΔABC is a right triangle, we can use the Pythagorean theorem to find the missing side, BC as shown below.

$\overline{BC}= \sqrt{20^{2} + 15^{2}} = 25$

Now, since AN is an altitude formed along BC, we can form two smaller triangles that are both similar with ΔABC.
(An image is attached along the file to show the illustrations of the triangles with the larger one.)

Thus, we have ΔNBA~ΔABC and ΔNAC~ΔABC. So, for ΔNBA and ΔABC, we have

$\frac{BN}{BA} = \frac{BA}{BC}$
$\frac{BN}{20} = \frac{20}{25}$
$\overline{BN} = \frac{20(20)}{25} = 16$

and applying the same process with AN, we have

$\frac{AN}{BA} = \frac{AC}{BC}$
$\frac{AN}{20} = \frac{15}{25}$
$\overline{AN} = \frac{20(15)}{25} = 12$

We can also use the same method to find the missing sides in ΔANC. But, we can immediately find the value of NC as shown.

$\overline{NC} = \overline{BC} - \overline{BN}$
$\overline{NC} = 25 - 16 = 9$

Since ΔANC is a right triangle and two given lengths, we can find the third side, AN, through Pythagorean theorem.

$\overline{AN} = \sqrt{15^{2} - 12^{2}} = 9$

Thus, we have found all the missing sides. The picture attached also shows the missing sides' lengths in red.

Answer: BC = 25, BN = 16, NC = 9, and AN = 12