Respuesta :
Given
5x+2y=16 ---(1)
7.5x+3y=24 ----(2)
Find
1) value of x and y
2) Type of system
Explanation
From equation (1)
[tex]\begin{gathered} 5x+2y=16 \\ 5x=16-2y \\ x=\frac{16-2y}{5} \end{gathered}[/tex]Putting this value of x in equation 2
[tex]\begin{gathered} 7.5x+3y=24 \\ 7.5(\frac{16-2y}{5})+3y=24 \\ 1.5(16-2y)+3y=24 \\ 24-3y+3y=24 \end{gathered}[/tex]From here we cannot find the values of x and y as 3y and -3y will cancel each other. Hence there is not a particular solution
Checking the type of system
From these equations we get
[tex]\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}[/tex]Therefore the lines are coincident to each other
Therefore the lines have infinte solutions
Final Answer
Therefore the lines have infinte solutions
The lines are coincident to each other
