Question

Select the best possible first step to solving the system by first eliminating the x variable. 4x 9y = 21 3x − 8y = 1 multiply the first equation by 3, and multiply the second equation by 4. multiply the first equation by −3, and multiply the second equation by −4. multiply the first equation by 8, and multiply the second equation by 9. none of the above

Answer 1

Answer: The correct option is

(A) multiply the first equation by 3, and multiply the second equation by 4.

Step-by-step explanation: The given system of linear equations is:

`4x+9y=21~~~~~~~~~~~~~~~~(i)\\\\3x-8y=1~~~~~~~~~~~~~~~~~(ii)`

We are to select the best possible first step to solve the above system by first eliminating x variable.

Since, we need to eliminate x variable first, so will try to make the coefficients of x in both the equations equal. After that, we will subtract one of the equations from the other to eliminate x.

The co-efficient of x in equation (i) is 4,

and

the co-efficient of x in equation (ii) is 3.

So, to make both of them same, we will take the LCM of the coefficients 4 and 3.

We have

LCM(4, 3) = 12.

Now, we will multiply equation (i) by 3 and equation (ii) by 4 to make both the coefficients in equation (i) and (ii) equal to 12.

Thus, we will multiply first equation by 3 and second equation by 4.

Option (A) is CORRECT.

Answer 2

multiply the first equation by 3, and multiply the second equation by 4.