Question

Please help

Does the following system have a unique solution? Why?

4x-6y=-7

-2x+3y=18

A.No, because the determinant of the coefficient matrix is 12.
B.No, because the determinant of the coefficient matrix is 0.
C.Yes, because the determinant of the coefficient matrix is 12.
D.Yes, because the determinant of the coefficient matrix is 0.

Answer 1

so, what's the determinant of the coefficient matrix?

Answer 2

determinent of coefficient marrix=12-(-6)(-2)=12-12=0
\[now \frac{ a1 }{ a2 }=\frac{ b1 }{ b2 }\neq \frac{ c1 }{c2 },no solution\]
verify it.

Answer 3

oo ok so it B than

Answer 4

when determinent of a matrix is 0, two cases arise
case1.
\[\frac{ a1 }{a2 }=\frac{ b1 }{ b2 }=\frac{ c1 }{ c2 }, then infinite solutions.\]
case2.
\[\frac{ a1 }{ a2 }=\frac{ b1 }{ b2 }\neq \frac{ c1 }{ c2 },then no solutions.\]
where a1x+b1y=c1 and
a2x+b2y=c2

Answer 5

o ok then it must be D.

Answer 6

no it was B,I only gave more information.

Answer 7

O ok Im sorry

Answer 8

\[\frac{ 4 }{ -2 }=\frac{- 6 }{ 3 }=\frac{ -7 }{18 }\]
\[-2=-2\neq \frac{ -7 }{18 }\]
hence it has no solution.