Given,
The two lines intersect at the point (6,2).
To find: Check the linear equations.
Solution:
The given equations
[tex]\begin{gathered} -5x+9y=-12.......(1) \\ 3x+2y=22.......(2) \end{gathered}[/tex]
Multiply the equation (1) by 3 and equation (2) by 5.
[tex]\begin{gathered} -15x+27y=-36.........(3) \\ 15x+10y=110....(4) \end{gathered}[/tex]
Add both equations (3) and (4)
[tex]\begin{gathered} 37y=74 \\ y=2 \end{gathered}[/tex]
Put y = 2 in equation (2)
[tex]\begin{gathered} 3x+2\times2=22 \\ 3x=22-4 \\ 3x=18 \\ x=6 \end{gathered}[/tex]
Hence, the value of x and y is 6 and 2.
Thus, the given option (c) is correct.
