What is the answer to this math problem

Mathematics

1 answer:

shutvik [7]3 years ago

4 0

Y + x = 5x + 3
12 - y = x + 2y

Isolate x in the first equation, then substitute its expression into the second equation to find y:

y + x = 5x + 3
x = 5x - y + 3
-4x = -y + 3
x = y - 3/4

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12 - y = x + 2y
12 - y = (y - 3/4) + 2y
48 - 4y = y - 3 + 8y
48 - 4y = 9y - 3
-4y = 9y -51
-13y = -51
y = 51/13

Substitute this into the first equation to find x:

51/13 + x = 5x + 3
x - 5x = 3 - 51/13
-4x = -12/13
x = 3/13

Lastly, substitute back into both original equations to check work;

y + x = 5x + 3 --> 51/13 + 3/13 = 5(3/13) + 3 --> 54/13 = 54/13
12 - y = x + 2y --> 12 - 51/13 = 3/13 + 2(51/13) --> 105/13 = 105/13

Answer:
x = 3/13
y = 51/13

Hope this helps.

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Question 9: Variables: (smallest) s, q, r (largest)

Question 10: 5 whole numbers (7, 8, 9, 10, and 11)

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For question 10, it states $\frac{1}{4}$ . This can be split into $\frac{3}{x}$ and $\frac{3}{x}$ . When x is 12 in the first equation then $\frac{3}{12} = \frac{1}{4}$ and when x is 6 in the second equation $\frac{3}{6} =0.5$ (0.5 is also $\frac{1}{2}$ ). Therefore, x must be a whole number less than 12 and greater than 6, and it cannot be either 12 or 6. Whole numbers between 6 and 12 are 7, 8, 9, 10, and 11 or 5 whole numbers.