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nordsb [41]
3 years ago
5

Solve the system by the substitution method. -12x - 2y = -4 6x + 3y = 18

Mathematics
1 answer:
schepotkina [342]3 years ago
5 0

Answer: x = -1 , y = 8✔️

Step-by-step explanation:

-12x - 2y = -4 } Equation 1

6x + 3y = 18 } Equation 2

<em>We can extract the value of x from the equation 2: </em>

6x + 3y = 18 } Equation 2

6x = 18 - 3y

x = (18 - 3y)/6 } Equation 2

<em>Then we can substitute this value of x in equation 1: </em>

-12x - 2y = -4 } Equation 1

-12·(18 - 3y)/6 - 2y = -4

-36 + 6y -2y = -4

4y = -4 + 36

4y = 32

y = 32/4 = 8

<em>Now we can substitute this value of y in equation 2: </em>

x = (18 - 3y)/6 } Equation 2

x = (18 - 3·8)/6 = (18 -24)/6 = -6/6 = -1

Answer: x = -1 , y = 8✔️

<h3>Check </h3>

<em>We can check this result by substituting these values of x and y into the equations: </em>

-12x - 2y = -4 } Equation 1  

-12·(-1) - 2·8 = -4 ► 12 - 16 = -4✔️ checked!

6x + 3y = 18 } Equation 2

6·(-1) + 3·8 = 18 ► -6 + 24 = 18✔️ checked!

<h2><em>Spymore</em></h2>
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Find the HCF and LCM of 126 and 234?
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Below in bold.

Step-by-step explanation:

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2 years ago
Can you help me pleeeeaaassee??
melamori03 [73]

Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC, Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1), Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.

Given: The diagram is given and we need to find the errors and then fix them. Also ΔTSR ≈ ΔTCD

Let's solve the given question:

Given that ΔTSR ≈ ΔTCD

So we know by the properties of the similarity that if two triangles are similar then the ratio of their corresponding sides is equal.

So, ΔTSR ≈ ΔTCD

=> RT / TD = ST / TC

=> 14 / 7 = 16 / (x - 1)

In the question, we can observe that the given side ratio is DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC.

The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).

The third error is the value of x.

We can find the correct value of x from the given equation:

14 / 7 = 16 / (x - 1)

=> 2 = 16 / (x - 1)

Multiplying both sides by (x - 1):

(x - 1) × 2 = 16 / (x - 1) × (x - 1)

=> 2(x - 1) = 16

Multiplying both sides by 1 / 2:

2(x - 1) × 1 / 2= 16 × 1 / 2

=> x - 1 = 8

Adding 1 on both sides:

x - 1 + 1 = 8 + 1

x = 9

Therefore x = 9.

Hence the errors are:

Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC

Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).

Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.

Know more about "similar triangles" here: brainly.com/question/14366937

#SPJ9

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Step-by-step explanation:

For any triangle, the sum of the two legs must be greater than the hypotenuse. Otherwise the two legs would not be long enough to touch.

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