Question

alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. which linear combination of alvin’s system of equations reveals the number of solutions to the system? 9x 4y

Answer 1

When Alvin multiplies the first equation by 2 and the second equation by -3, the system of equations becomes 6x + 8y = 16 and -12x - 24y = -48. The linear combination 12x = 0 reveals that the system has infinitely many solutions.

Step-by-step explanation:

When Alvin multiplies the first equation by 2 and the second equation by -3, the system of equations becomes:

6x + 8y = 16

-12x - 24y = -48

To find the linear combination that reveals the number of solutions to the system, we can multiply the first equation by 6 and the second equation by 2:

36x + 48y = 96

-24x - 48y = -96

Adding these equations together, we get 12x = 0. This means that x = 0. When we substitute x = 0 into the first equation, we get 8y = 16, or y = 2.

Therefore, the linear combination 12x = 0 reveals that the system has infinitely many solutions.

Answer 2

The new linear combination of Alvin's system of equation is: 8y - 7.5y = 0. The value of x = 4 and y = 0.

Solving linear equation using elimination method.

In the given system of linear equation, Alvin multiplied the first equation by 2 and the second equation by -3 i.e

9x + 4y = 36 :×2

6x + 2.5y = 24 : -3

18x + 8y = 72

-18x - 7.5y = 72

Thus, the new linear combination of Alvin's system of equation is:

8y - 7.5y = 0

0.5y = 0

Divide both sides by 0.5

y = 0

From (9x + 4y=36), replace y with 0;

9x + 4(0) = 36

9x = 36

x = 36/9

x = 4

Here is the complete question.

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?

9x + 4y = 36

6x + 2.5y = 24