Question

Suppose you chose to solve the following system of questions by multiplying the first equation by 3. Then by what number would you multiple the second equation to eliminate the x variable by adding

Answer 1

Step-by-step explanation: Here we are multiplying the second equation by a number and then we will add both equations and our intention is to eliminate the variable "x" of the result of the sum.

Step 1: First let's get the result of the multiplication of the first equation by 3 as follows

`\begin{gathered} 4x-3x=\mleft(6\mright) \\ \mleft(4x-3x\mright)\mleft(3\mright)=\mleft(6\mright)\mleft(3\mright) \\ 12x-9x=18 \end{gathered}`

Step 2: As we can see we have a 12x on the first equation (after multiplying by 3) and a 6x on the second one so we just need to find a number that multiplies 6x that gives us -12x once 12x + (-12x) = 0x.

We can see that 6x * (-2) = -12x

So the have

`\begin{gathered} 6x+y=10 \\ (6x+y)(-2)=10(-2) \\ -12x-2y=-20 \end{gathered}`

Above we have our second equation after multiplying it by -2

Step 3: Now we can try to sum both equations to see if it works as expected

see the calculation below

Final answer: As we can see above our assumption was right so the final answer is -2