1

Problem

Solve for x and y in the system of linear equations:

11x + 9y = 18 and 8x - 12y = 10.

2

Step

The given equation (1) is:

11x + 9y = 18

3

Step

The given equation (2) is:

8x - 12y = 10

4

Step

Multiply equation (1) by 12 to yield equation (3):

132x + 108y = 216

5

Step

Multiply equation (2) by 12 to yield equation (4):

72x - 108y = 90

6

Step

Add equation (3) and equation (4):

132x + 108y + 72x - 108y = 216 + 90

7

Step

After simplification:

204x + 0 = 306

8

Step

Move the x coefficient to the right side, then solve for x:

204x = 306

\$ "x" = 3/2 \$

9

Step

Substituting the value of x in equation (1), then we get y value:

16.5 + 9y = 18

\$ "y" = 1/ 6 \$

10

Solution

So, the x and y values are \$3/2\$ and \$1/6\$.

11

Sumup

Please summarize steps

12

Choice-A

This option suggests the solution is \$"x" = 2/3\$ and \$"y" = 5/6\$. However, after solving the system of equations, we found that \$"x" = 3/2\$ and \$"y" = 1/6\$, so this option is incorrect

Wrong \$"x" = 2/3\$ and \$"y" = 5/6 \$

13

Choice-B

This option suggests the solution is \$"x" = 3/2\$ and \$"y" = 1/6\$. After solving the system of equations, we found that \$"x" = 3/2\$ and \$"y" = 1/6\$, so this option is correct

Correct \$x = 3/2\$ and \$"y" = 1/6 \$

14

Choice-C

This option suggests the solution is \$"x" = 2/3\$ and \$"y" = -5/6\$. After solving the system of equations, we found that \$"x" = 3/2\$ and \$"y" = 1/6\$, so this option is incorrect

Wrong \$"x" = 2/3\$ and \$"y" = -5/6 \$

15

Choice-D

This option suggests the solution is \$"x" = -3/2\$ and \$"y" = 1/6\$. After solving the system of equations, we found that \$"x" = 3/2\$, not \$"y" = -3/2\$, so this option is incorrect

Wrong \$"x" = -3/2\$ and \$"y" = 1/6 \$

16

Answer

Option

B

17

Sumup

Please summarize choices