Question

Thuy wrote the system of equations

24x+3y = 72
- 18x+y = 30
If the second equation is multiplied by 3. What should the first equation be multiplied by to eliminate the x variable by
addition?

Answer 1

The answer on the test is 2

Explanation:

Answer 2

Equation (1) should be multiplied by (9/4) to eliminates the variable x by addition.

Explanation:

Here, the given system of equation is:

24 x + 3 y = 72

- 18 x + y = 30

Now, equation (2) x 3 = - 18(3) x + (3) y =(3) 30

⇒ -54 x + 3 y = 90

So, the x term = -54 x

Now, for x to be eliminated in the first term,

24 x should be transformed in to + 54 x as 54 x - 54 x = 0

Let us assume, 24x is multiplied by a factor m so that

24x (m) = 54 x

⇒
`m =  (54x)/(24x)  = (9)/(4)`

or, m = 9/4

Hence, equation (1) should be multiplied by (9/4) to eliminates the variable x by addition.