Question

I need help figuring out statements in algebra 2 please

Answer 1

The equations are given below as

`\begin{gathered} 2x+3y-46=22\ldots..(1) \\ 10-3y+6x=20\ldots..(2) \end{gathered}`

Step 1:

From equation (1), add 46 to both sides

`\begin{gathered} 2x+3y-46+46=22+46 \\ 2x+3y=68\ldots\text{.}(3) \end{gathered}`

Step 2:

From equation (2),substract 10 from both sides

`\begin{gathered} 10-10-3y+6x=20-10 \\ 6x-3y=10\ldots\text{.}(4) \end{gathered}`

Step 3:

Multiply equation (3) by 3

`\begin{gathered} 3(_{}2x+3y)=68*3 \\ 6x+9y=204\ldots\text{.}(5) \end{gathered}`

Step 4:

Substract equation (4) from equation (5)

`\begin{gathered} 6x+9y-(6x-3y)=204-10 \\ 6x-6x+9y+3y=194 \\ 12y=196 \\ (12y)/(12)=(194)/(12) \\ y=(97)/(6) \end{gathered}`

Step 5:

Substitute y= 97/6 in equation (4)

`\begin{gathered} 6x-3y=10 \\ 6x-3((97)/(6))=10 \\ 6x-(97)/(2)=10 \\ 6x=10+(97)/(2) \\ 6x=(20+97)/(2) \\ 6x=(117)/(2) \\ 12x=117 \\ (12x)/(12)=(117)/(12) \\ x=(39)/(4) \end{gathered}`

Hence,

The value of x=39/4 and y= 97/6

The solution system of equations has exactly one point