Question

Which of the following points is a solution to the following system of equations?

x + y = 1
3x – y = 3

A.
(3, 0)
B.
(5, –1)
C.
(1, 4)
D.
(1, 0)

Sally was asked to find two integers such that one is three less than 4 times the other and the sum of the two integers is 42. The integers must be _____.
A.
14, 28
B. 15, 27
C.
9, 33
D.
-13, 55

Answer 1

For the first one, you can plug in the solutions to see which one fits.

Answer 2

First part is D; (1)+(0)=1 and 3(1)-(0)=3, it satisfies both conditions.

Answer 3

x + y = 1

(3, 0)

3 + 0 = 1

3 = 1

That's wrong.

(1, 0)

x + y = 1

1 + 0 = 1

1 = 1

Correct.

Check the other equation:

3x – y = 3

3(1) – 0 = 3

3 - 0 = 3

3 = 3

So the answer to the first one is (1, 0)

Answer 4

Second part is C; make an expression representing both integers, x for first integer, and (4x-3) for second one. The sum is 42, so x+4x-3=42 -> 5x=45, therefore x=9. Plug in this value for (4x-3) and you get 4(9)-3=33. So your integers are 9 and 33.

Answer 5

Sally was asked to find two integers such that one is THREE LESS THAN 4 TIMES the other and the SUM OF THE TWO INTEGERS IS 42.

Let's test out the first one:

14, 28

4 * 28 = 112

4 * 14 = 56

Incorrect.

15, 27

4 * 27 = 108

4 * 15 = 60

Incorrect.

9, 33

4 * 33 = 132

4 * 9 = 36

Correct so far.

9 + 33 = 42.

So the correct answer for the second one is (9, 33)

Answer 6

thank you so much