If the system of equations 2x + 3y = -1,3x + | vedclass

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(A) Given the system of equations:$2x + 3y = -1$  $(1)$$3x + y = 2$  $(2)$$\lambda x + 2y = \mu$  $(3)$First,solve equations $(1)$ and $(2)$ to find t

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$\lambda - \mu = 2$

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(A) Given the system of equations:$2x + 3y = -1$  $(1)$$3x + y = 2$  $(2)$$\lambda x + 2y = \mu$  $(3)$First,solve equations $(1)$ and $(2)$ to find the point of intersection $(x, y)$.From $(2)$,$y = 2 - 3x$.Substitute this into $(1)$:$2x + 3(2 - 3x) = -1$$2x + 6 - 9x = -1$$-7x = -7 \Rightarrow x = 1$.Now,find $y$:$y = 2 - 3(1) = -1$.Since the system is consistent,the point $(1, -1)$ must satisfy the third equation $(3)$:$\lambda(1) + 2(-1) = \mu$$\lambda - 2 = \mu$$\lambda - \mu = 2$.

If the system of equations $2x + 3y = -1$,$3x + y = 2$,and $\lambda x + 2y = \mu$ is consistent,then:

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