Question

3x + 4y = 14 x = 2y - 12 Which point satisfies both equations? A) (-2,-2) B) (-2,5) C) (-4,4) D) (2,2)

Answer 1

x = -2

y = 5

then:

B) (-2,5)

Explanation:

3x + 4y = 14

x = 2y - 12

from te firs equation:

3x = 14 - 4y

x = (14-4y)/3

then:

2y - 12 = (14-4y)/3

3(2y-12) = 14 - 4y

3*2y + 3*-12 = 14 - 4y

6y - 36 = -4y + 14

6y + 4y = 14 + 36

10y = 50

y = 50/10

y = 5

from the second equation:

x = 2y - 12

x = 2*5 - 12

x = 10 - 12

x = -2

Check:

from the first equatión:

3x + 4y = 14

3*-2 + 4*5 = 14

-6 + 20 = 14

Answer 2

B) (-2, 5)

Explanation:

Perhaps easiest is to try the points to see what works. You can also graph the equations or solve by any of several other means.

Trying the points

A) 3(-2)+4(-2) = -6 -8 = -14 ≠ 14

B) 3(-2) +4(5) = -6 +20 = 14; -2 = 2(5) -12 = 10 -12 . . . . true

C) 3(-4) +4(4) = -12 +16 = 4 ≠ 14

D) 3(2) +4(2) = 6 +8 = 14; 2(2) -12 = -8 ≠ -2

__

Choice B ( -2, 5) is the only point that works in both equations.