Question

8. Which point is a solution to the system of equations shown below?

(1) (3,7)
(2) (0,1)
(3) (1,5)
(4) (2,3)

y=-2x+7
y = 4x-5

Answer 1

• Answer:

`\red{\boxed{ \green{\sf Option \: 4: (2 \: , 3)}}}`

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• Step-by-step explanation:

`\sf First, \: we \: have \: to \: understand \: that: \\ \sf If \: \red{y} = \orange{a} \: and \: \red{y} = \blue{b}, \: then \: \orange{a} = \blue{b}.`

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`\sf Let \: \orange{-2x+7} \: be \: \orange{a} \: and \: \blue{4x-5 \\ } \: be \: \blue{b}.`

`\star \: \sf Solve \: the \: equation \: \orange{a} = \blue{b}. \: \star`

`\\`

`\sf \orange{a} = \blue{b} \\ \Longleftrightarrow \sf \orange{ - 2x + 7} = \blue{4x - 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Subtract \: 4x \: from \: both \: sides. \diamond \\ \\ \Longleftrightarrow \sf - 6x + 7 = - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Subtract \: 7 \: from \: both \: sides. \diamond \\ \\ \Longleftrightarrow \sf - 6x = - 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Divide \: both \: sides \: by \: -6. \: \diamond \\ \\ \Longleftrightarrow \sf x = ( - 12)/( - 6) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \Longleftrightarrow \boxed{\sf \purple{x = 2}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:`

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`\star \: \sf Remplace \: \purple{x} \: with \: \purple{2} \: in \: one \: of \: the \: given \: equations. \: \star`

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`\sf \red{y }= - 2 \purple{x} + 7 \\ \implies \sf \red{y} = - 2 \purple{(2)} + 7 \: \: \: \: \: \: \\ \\ \implies \boxed{\sf \red{y= 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:`

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Therefore, the point which is a solution to the system of equations is (2 , 3). This corresponds to option 4.

Answer 2

option (4)

Step-by-step explanation:

y = - 2x +7 → (1)

y = 4x - 5 → (2)

substitute y = 4x - 5 into (1)

4x - 5 = - 2x + 7 ( add 2x to both sides )

6x - 5 = 7 ( add 5 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

y = 4(2) - 5 = 8 - 5 = 3

solution is (2, 3 )