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Which ordered pair is the best estimate for the solution of the system of equations? The graph of the system of equations : y = 3/2x +6 AND y=1/4x - 2 a.(-6, -3) b.(-6.5, -3.5) c.(-7, -4) d.(-7, -3.5)

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kudzordzifrancis
ANSWER

Option C is the best estimate for the solution


EXPLANATION

The given system of equations is

[tex]y = \frac{3}{2}x + 6...(1)[/tex]
and

[tex]y = \frac{1}{4}x - 2[/tex]


We equate the two equation to get,



[tex]\frac{3}{2}x + 6=\frac{1}{4}x - 2[/tex]



We group the like terns to get,


[tex]\frac{3}{2}x - \frac{1}{4}x = - 2 - 6[/tex]



[tex]\frac{3}{2}x - \frac{1}{4}x = - 8[/tex]




[tex]4 \times \frac{3}{2}x - 4 \times \frac{1}{4}x = - 8 \times 4[/tex]



[tex]6x - x = - 32[/tex]

[tex]5x = - 32[/tex]


[tex]x = - 6.4[/tex]


We put
[tex]x = - \frac{32}{5} [/tex]

into equation 2 to get,


[tex]y = \frac{1}{4} \times - \frac{32}{5} - 2[/tex]



[tex]y = - \frac{18}{5} [/tex]



[tex]y = - 3.6[/tex]


Rounding to the nearest tenth we get

[tex]x = - 7 \: and \: y = - 4[/tex]

Answer: b

Step-by-step explanation: I took the test