Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

11x + 8y = 103
22x – 7y = 68

Double the first equation (on both sides) to obtain

22x + 16y = 206

Then subtract the second equation from the above (on both sides) to eliminate the variable x.

23y = 138

They solve for y.

Then use any of the original equations to solve for x.

Show your work for further assistance.

Radical 10, please don't repost questions! I took the time to solve this for you when it was already done.

To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the two equations.

First, let's multiply the second equation by 2 to make the coefficients of x in both equations the same:

2(22x – 7y) = 2(68)
44x – 14y = 136

Now we have the two equations:
11x + 8y = 103
44x - 14y = 136

To eliminate the variable y, we can add the two equations together:

(11x + 8y) + (44x - 14y) = 103 + 136
55x - 6y = 239

Now we have the following system of equations:
55x - 6y = 239
11x + 8y = 103

To eliminate y, we need the coefficients of y to be the same but with opposite signs. Currently, the coefficients are -6 and 8. We can multiply both sides of the second equation by 3 to make the coefficients -6 and -6:

3(11x + 8y) = 3(103)
33x + 24y = 309

Now we have the following system of equations:
55x - 6y = 239
33x + 24y = 309

Next, we can add the two equations together to eliminate y:

(55x - 6y) + (33x + 24y) = 239 + 309
88x + 18y = 548

Now we have the following equation:
88x + 18y = 548

We have eliminated the variable y, but we still have a variable x. Therefore, we cannot solve this system using the elimination method.

To solve this system of equations using the elimination method, we need to eliminate one of the variables by manipulating the two equations in a way that the coefficients of one variable in both equations become additive inverses of each other. Here's how we can do it:

First, let's multiply the second equation by 2 to make the coefficients of x in both equations equal:

2(22x – 7y) = 2(68)
44x – 14y = 136

Now, we have the system of equations:

11x + 8y = 103
44x – 14y = 136

Next, we can add the two equations together to eliminate the y variable:

(11x + 8y) + (44x – 14y) = 103 + 136
55x – 6y = 239

Now, we have the new equation:

55x – 6y = 239

Let's multiply the first equation by 6 to make the coefficients of y in both equations equal:

6(11x + 8y) = 6(103)
66x + 48y = 618

Now, we have the system of equations:

66x + 48y = 618
55x – 6y = 239

We can multiply the second equation by -8 to make the coefficients of y in both equations additive inverses:

-8(55x – 6y) = -8(239)
-440x + 48y = -1912

Now, we have the new equation:

-440x + 48y = -1912

Finally, let's add the two equations together:

(66x + 48y) + (-440x + 48y) = 618 + (-1912)
-374x = -1294

Divide both sides of the equation by -374 to solve for x:

x = -1294 / -374
x = 3.46 (rounded to two decimal places)

Now, substitute this value of x back into one of the original equations to find the value of y. Let's use the first equation:

11x + 8y = 103
11(3.46) + 8y = 103
38.06 + 8y = 103
8y = 103 - 38.06
8y = 64.94
y = 64.94 / 8
y = 8.12 (rounded to two decimal places)

Therefore, the solution to the system of equations is x = 3.46 and y = 8.12.

There is no need to state that the system has no solution or an infinite number of solutions as we have obtained unique values for both x and y.