Question

What is the value of y in this system of equations: 3x + y = 9 y = –4x + 10 ?

Answer 1

3x + y = 9 (I)
y = –4x + 10 (II)
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`\left \{ {{3x + y = 9 } \atop {y = -4x + 10 }} \right.`

Pass the incognito "4x" to the first term, changing the signal when changing sides.
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simplify by (-1)

`\left \{ {{3x + y = 9.(-1)} \atop {4x + y = 10 }} \right.`

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`\left \{ {{- 3x - \diagup\!\!\!\!y =-9} \atop {4x + \diagup\!\!\!\!y = 10}} \right.`

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`\left \{ {{- 3x = - 9} \atop {4x = 10}} \right.`

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`\boxed{x = 1}`

Substitute in equation (I) to find the value of "Y".

3x + y = 9 (I)
3*(1) + y = 9
3 + y = 9
y = 9 - 3

`\boxed{y = 6}`

Answer:

`\boxed{\boxed{ \left \ {{x=1} \atop {y=6}} \right. }}`