Question

Which of the following steps would you perform to the system of equationsbelow so that the equations have equal x-coefficients?4x+2y = 412x + y = 22A. Divide both sides of the top equation by 3 byB. Multiply both sides of the bottom equation by 3C. Divide both sides of the bottom equation by 2b byD. Multiply both sides of the top equation by 3

Answer 1

D. Multiply both sides of the top equation by 3

Step-by-step explanation

`\begin{gathered} 4x+2y=4 \\ 12x+y=22 \end{gathered}`

to do that, both equations must have equal x-coeeficient, we need

Step 1

check the coefficients

`\begin{gathered} 4x+2y=4\Rightarrow x\text{ coefficient is 4} \\ 12x+y=22\Rightarrow x\text{ coefficient is 12} \end{gathered}`
`\begin{gathered} c_1=4 \\ c_2=12 \end{gathered}`

Now, to go from C1 ( 4) to C2( 12) we can multiply the top eqution by 3 , this way we would get

`\begin{gathered} 3\cdot c_1=12 \\ 3\cdot c_1=c_2 \\ 12=12 \end{gathered}`

or

to go from C2 ( 12) to C1 ( 3) we can divide the bottom equation by 3

`\begin{gathered} c_1=(1)/(3)\cdot c_2 \\ 4=(12)/(3) \\ 4=4 \end{gathered}`

therefore, the anwer is

D. Multiply both sides of the top equation by 3

`3\cdot(4x+2y=4)\Rightarrow12x+8y=12`

now it has 12 as coefficient for x

I hope this helps you