Solution:
The equations are given below as
[tex]\begin{gathered} 2x+3y-46=22\ldots..(1) \\ 10-3y+6x=20\ldots..(2) \end{gathered}[/tex]
Step 1:
From equation (1), add 46 to both sides
[tex]\begin{gathered} 2x+3y-46+46=22+46 \\ 2x+3y=68\ldots\text{.}(3) \end{gathered}[/tex]
Step 2:
From equation (2),substract 10 from both sides
[tex]\begin{gathered} 10-10-3y+6x=20-10 \\ 6x-3y=10\ldots\text{.}(4) \end{gathered}[/tex]
Step 3:
Multiply equation (3) by 3
[tex]\begin{gathered} 3(_{}2x+3y)=68\times3 \\ 6x+9y=204\ldots\text{.}(5) \end{gathered}[/tex]
Step 4:
Substract equation (4) from equation (5)
[tex]\begin{gathered} 6x+9y-(6x-3y)=204-10 \\ 6x-6x+9y+3y=194 \\ 12y=196 \\ \frac{12y}{12}=\frac{194}{12} \\ y=\frac{97}{6} \end{gathered}[/tex]
Step 5:
Substitute y= 97/6 in equation (4)
[tex]\begin{gathered} 6x-3y=10 \\ 6x-3(\frac{97}{6})=10 \\ 6x-\frac{97}{2}=10 \\ 6x=10+\frac{97}{2} \\ 6x=\frac{20+97}{2} \\ 6x=\frac{117}{2} \\ 12x=117 \\ \frac{12x}{12}=\frac{117}{12} \\ x=\frac{39}{4} \end{gathered}[/tex]
Hence,
The value of x=39/4 and y= 97/6
The solution system of equations has exactly one point
