Question

To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied?

First Equation: 5x − 4y = 28

Second equation: 3x - 9y = 30

The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 3 and the second equation by −5.
The first equation should be multiplied by 9 and the second equation by 4.
The first equation should be multiplied by 9 and the second equation by −4.

Answer 1

the answer is D

Explanation:

Answer 2

The first equation should be multiplied by 9 and the second equation by 4

9(5x - 4y) = 9(28)
4(3x - 9y) = 4(30)

45x - 36y = 252 ⇒ 45x - 36y = 252
-(12x - 36y = 120)⇒ -12x + 36y = -120
33x + 0 = 132

33x = 132
x = 132/33
x = 4

5x - 4y = 28
5(4) - 4y = 28
20 - 4y = 28
-4y = 28 - 20
-4y = 8
y = 8/-4
y = -2

x = 4 ; y = -2

3x - 9y = 30
3(4) - 9(-2) = 30
12 + 18 = 30
30 = 30