Question

Which system of equations is graphed below? On a coordinate plane, a line goes through (0, 1) and (4, negative 2) and another goes through (0, negative 6) and (6, 0). x minus y = 6. 4 x + 3 y = 1. x minus y = 6. 3 x + 4 y = 4. x + y = 6. 4 x minus 3 y = 3. x + y = 6. 3 x minus 4 y = 4.

Answer 1

14.5, 13, 11.5

Explanation:

the general term (an) of an arithmetic sequence with first term a1 and common difference d is

an = a1 + d(n-1)

then the 8th term is

a8 = a1 + d(8-1)

and the 12th term is

a12 = a1 + d(12-1)

so, the difference between these terms is

a12 -a8 = (a1 +11d) -(a1 +7d) = 4d

= (-2-4) = -6 . . . substituting values for a12 and a8

then the common difference is

d = -6/4 = -3/2

using this, we can find a1 from a8.

4 = a1 +7·(-3/2) = a1 - 10.5

14.5 = a1 . . . . add 10.5 to both sides of the equation

this is the first term. the second is this value with the common difference added:

14.5 + (-1.5) = 13

the third term is this with the common difference added:

13 + (-1.5) = 11.5

in summary, the first three terms are

14.5, 13, 11.5

Answer 2

a)x - y = 6. 4 x + 3 y = 1.

Explanation:

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