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Which set of coordinates satisfies the system of equations y = x − 3 and y = -2x + 1?

Sagot :

Given:

The system of equations is

[tex]y=x-3[/tex]         ...(i)

[tex]y=-2x+1[/tex]         ...(ii)

To find:

The set of coordinates that satisfies the system of equations.

Solution:

On equating the given equations, we get

[tex]x-3=-2x+1[/tex]

[tex]x+2x=3+1[/tex]

[tex]3x=4[/tex]

Divide both sides by 3.

[tex]x=\dfrac{4}{3}[/tex]

Putting [tex]x=\dfrac{4}{3}[/tex] in (i), we get

[tex]y=\dfrac{4}{3}-3[/tex]

[tex]y=\dfrac{4-9}{3}[/tex]

[tex]y=\dfrac{-5}{3}[/tex]

Therefore, the required set of coordinates that satisfies the given system of equations is [tex]\left(\dfrac{4}{3},\dfrac{-5}{3}\right)[/tex].

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