Question

9
for which system of equations is (-3, 5) the solution?
hint: you do not have to solve them all algebraically! graph them and look for the intersection ;)
a
\

$$\begin{cases}2x + y = -1\\\\x + 2y = 7\\end{cases}$$

b
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$$\begin{cases}5x - 3y = 12\\\\2x + 3y = 18\\end{cases}$$

c
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$$\begin{cases}3x + 2y = 1\\\\6x - 4y = 2\\end{cases}$$

d
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$$\begin{cases}4x - 3y = -27\\\\2x + 4y = 12\\end{cases}$$

Explanation:

Step1: Test (-3,5) in System A

Substitute $x=-3$, $y=5$:
First equation: $2(-3)+5=-6+5=-1$ (matches)
Second equation: $-3+2(5)=-3+10=7$ (matches)

Step2: Verify other systems (optional check)

System B: $5(-3)-3(5)=-15-15=-30
eq12$ (fails)
System C: $3(-3)+2(5)=-9+10=1$ (matches first), $6(-3)-4(5)=-18-20=-38
eq2$ (fails)
System D: $4(-3)-3(5)=-12-15=-27$ (matches first), $2(-3)+4(5)=-6+20=14
eq12$ (fails)

Answer:

A.

$$\begin{cases} 2x + y = -1 \\ x + 2y = 7 \end{cases}$$