Question

1. identify a solution to this system of equations: \\(\

$$\begin{cases}-4x + 3y = 23\\x - y=-7\\end{cases}$$

\
a (-5, 2)\
b (-2, 5)\
c (-3, 4)\
d (4, -3)\

1. lin is solving this system of equations: \\(\

$$\begin{cases}6x - 5y = 34\\3x + 2y = 8\\end{cases}$$

\
she starts by rearranging the second equation to isolate the y variable: y = 4 - 1.5x.\
she then substituted the expression 4 - 1.5x for y in the first equation, as shown:\
6x - 5(4 - 1.5x) = 34\
6x - 20 - 7.5x = 34\
-1.5x = 54\
x=-36\
y = 4 - 1.5x\
y = 4 - 1.5\cdot(-36)\
y = 58\
a. check to see if lins solution of (-36, 58) makes both equations in the system true.\
b. if your answer to the previous question is
o,\ find and explain her mistake. if your answer is \yes,\ graph the equations to verify the solution of the system.

Explanation:

Step1: Check solution for first - equation of first system

Substitute \(x=-5\) and \(y = 2\) into \(-4x + 3y\):
\(-4\times(-5)+3\times2=20 + 6=26
eq23\)
Substitute \(x=-2\) and \(y = 5\) into \(-4x + 3y\):
\(-4\times(-2)+3\times5=8 + 15=23\)
Substitute \(x=-2\) and \(y = 5\) into \(x - y\):
\(-2-5=-7\)
So \((-2,5)\) is a solution of the first system of equations.

Step2: Check Lin's solution for first equation of second system

Substitute \(x=-36\) and \(y = 58\) into \(6x-5y\):
\(6\times(-36)-5\times58=-216-290=-506
eq34\)
The error in Lin's work is in the step \(6x - 5(4 - 1.5x)=34\) when distributing the \(-5\).
It should be \(6x-20 + 7.5x=34\), not \(6x-20 - 7.5x=34\).

Answer:

1. B. \((-2,5)\)
2. a. No.

b. The mistake is in the distribution of \(-5\) in \(6x - 5(4 - 1.5x)=34\). It should be \(6x-20 + 7.5x=34\) instead of \(6x-20 - 7.5x=34\).