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7nadin3 [17]
3 years ago
8

Show the processes for solving 2x+3y=5 and 4x - y=17 using elimination and substitution

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
7 0

<u>ANSWER:  </u>

The solution of the two equations 2x+3y=5 and 4x - y=17 is (4, -1).

<u>SOLUTION: </u>

Given, two linear equations are 2x + 3y = 5 → (1) and 4x – y = 17 → (2).

Let us first solve the above equations using <em>elimination process. </em>

For elimination, one of the coefficients of variables has to be same in order to cancel them.

Now solve (1) and (2)

eqn (1) \times 2 → 4x + 6y = 10

eqn (2) → 4x – y = 17

(-) ----------------------------

     0x + 7y = -7

y = -1

Substitute y value in (2)

4 x-(-1)=17 \rightarrow 4 x+1=17 \rightarrow 4 x=17-1 \rightarrow 4 x=16 \rightarrow x=4

So, solution of two equations is (4, -1).

<u><em>Now let us solve using substitution process.</em></u>

Then, (2) → 4x – y = 17 → 4x = 17 + y → y = 4x – 17

Now substitute y value in (1) → 2x + 3(4x – 17) = 5 → 2x + 12x – 51 = 5 → 14x = 5 + 51 → 14x = 56  

x = 4

Substitute x value in (2) → y = 4(4) – 17 → y = 16 – 17 → y = -1

Hence, the solution of the two equations is (4, -1).

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Answer:

\sf 500,000,000,000=5 \times 10^{11}

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Step-by-step explanation:

<u>Scientific notation</u>

\large\boxed{a \times 10^n}  

where:

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To convert a number into scientific notation, <u>move</u> the decimal point to the <u>left or right</u> until there is <u>one digit</u> to the left of the decimal point.

The number of times you have moved the decimal point is n.

  • If the decimal point has moved to the <u>left</u>, n is positive.
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To convert 500,000,000,000 into scientific notation, move the decimal point <u>11 places to left</u>, so a = 5.  As we have moved the decimal point 11 places to the left, the exponent "n" is 11 and is <u>positive</u>.

\implies \sf 500,000,000,000=5 \times 10^{11}

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