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3 years ago

Solve the following simultaneous equations using an appropriate method.

Mathematics

2 answers:

Dimas [21]3 years ago

7 0

Good evening ,

Look at the photo below for the answer.

Reika [66]3 years ago

6 0

Answer:

a) x = 1 , y = 3

Step-by-step explanation:

a) 7x + 3y = 16

y = 4x - 1

3y + 7x = 16 ... (i)

y - 4x = -1 ... (ii)

Solving the simultaneous equation by substitution;

Equation (ii) tells us that y = 4x - 1

Substituting that in (i) gives;

3(4x - 1) + 7x = 16

12x - 3 + 7x = 16

19x = 16 + 3 = 19

x = $\frac{19}{19}$ = 1

y = 4(1) - 1 = 3

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What is the solution set of {x | x < -5} ∩ {x | x > 5}

Kisachek [45]

Answer:

The answer is: {x | x < -5} ∩ {x | x > 5}= { }.

Step-by-step explanation:

Let us first list the elements of the first set.

{x | x < -5} reads x is an element such that x is less than -5. So we list all the integers less than -5.

{x | x < -5}= {-6,-7,-8,-9,-10,-11,-12,-13,-14,...}

Similarly, we find the elements of the second set which reads: x is an element such that, x is greater than 5. So we list all integers greater than 5

{x | x > 5}= {6,7,8,9,10,11,12,13,14,...}

Finally we are required to find the numbers or elements in both sets that intersect or are the same with each other.

Since no element in both sets listed above intersect each other, the solution is an empty set:

Therefore, {x | x < -5} ∩ {x | x > 5}= { }.

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SpyIntel [72]

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4 years ago

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Elimination

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2x - 4y + 1z = 11 ⇒ 2x - 4y + 1z = 11
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 1x - 2y - 2z = 2
2x - 4y + 1z = 11 -2x + 2y - 2z = -3
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3x + 5z = 12 ⇒ 3x + 5z = 12 x - 4z + 4z = 1 + 4z
 -2x + 2y - 2z = -3 x = 1 + 4z
 1 + 4z - 2y - 2z = 2
 1 - 2y + 4z - 2z = 2
 1 - 2y + 2z = 2
 - 1 - 1
 -2y + 2z = 1
 -2y + 2z - 2z = 1 - 2z
 -2y = 1 - 2z
 -2 -2
 y = -0.5 + z
 x + 2(-0.5 + z) - 2z = 2
 x - 1 + z - 2z + 2 = 2
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 + 1 + 1
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4 0

4 years ago