Question

Choose the correct first step(s) to solve the system using elimination.
4x + 7y = 6 and 6x + y = 2

7(6x + y = 2) → -42x - 7y = -14
4x + 7y = 6x + y
y = -6x + 20 → 4x + 7(-6x + 20) = 6
(4x + 7y) + (6x + y) = 8
(4x + 7y) - (6x + y) = 4

Answer 1

in terms of x—1st & 2nd equations:
4x + 7y + 6x + y = 6 + 2
10x + 8y = 8
y = 1 - 5/4x

1st equation—x, substitute y:
4x + 7(1 - 5/4x) = 6
4x + 7 - 35/4x = 6
16x + 28 - 35x = 24
19x = 4
x = 4/19

Value of y, substitute x:
= 1 - 5/4(4/19)
= 19/19 - 5/19
= 14/19

Answer: x = 4/19, y = 14/19

Proof—2nd equation:
6(4/19) + 14/19 = 2
24/19 + 14/19 = 2
38/19 = 2
2 = 2

Answer 2

i think there may be a typo here

Answer 3

if the initial equations were
\[4x + 7y = 6 \]
\[6x + y = 20\] the a good first step would be
\[y = -6x + 20 → 4x + 7(-6x + 20) = 6 \]