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If -5x + 2y = 9 and 3x - 4y = -4, then what is the value of 7x + 10y ?

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Bunuel
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If -5x + 2y = 9 and 3x - 4y = -4, then what is the value of 7x + 10y ? [#permalink] New post   04 Jun 2021, 04:15
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If \(-5x+2y=9\) and \(3x-4y=-4\), then what is the value of \(7x+10y\)?

A. -19

B. -17

C. -9

D. 9

E. 19
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LaveenaPanchal
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Re: If -5x + 2y = 9 and 3x - 4y = -4, then what is the value of 7x + 10y ? [#permalink] New post   04 Jun 2021, 04:53
−5x+2y=9 So -10x+4y = 18
Adding -10x + 4y=18 and 3x−4y=−4, -7x =14 so x = -2

Putting x = -2 in -5x + 2y = 9, we get y = -1/2

The value of 7x + 10y = 7 (-2) + 10 x (-1/2) = -14 - 5 = -19

The answer is A -19
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AbhaGanu
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Re: If -5x + 2y = 9 and 3x - 4y = -4, then what is the value of 7x + 10y ? [#permalink] New post   04 Jun 2021, 07:52
LaveenaPanchal wrote:
−5x+2y=9 So -10x+4y = 18
Adding -10x + 4y=18 and 3x−4y=−4, -7x =14 so x = -2

Putting x = -2 in -5x + 2y = 9, we get y = -1/2

The value of 7x + 10y = 7 (-2) + 10 x (-1/2) = -14 - 5 = -19

The answer is A -19



Hi! How did you get this value? -10x + 4y=18? WHy did you multipy all numbers by 2?
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If -5x + 2y = 9 and 3x - 4y = -4, then what is the value of 7x + 10y ? [#permalink] New post   07 Apr 2023, 22:31
AbhaGanu wrote:
LaveenaPanchal wrote:
−5x+2y=9 So -10x+4y = 18
Adding -10x + 4y=18 and 3x−4y=−4, -7x =14 so x = -2

Putting x = -2 in -5x + 2y = 9, we get y = -1/2

The value of 7x + 10y = 7 (-2) + 10 x (-1/2) = -14 - 5 = -19

The answer is A -19



Hi! How did you get this value? -10x + 4y=18? WHy did you multipy all numbers by 2?


You can multiply all the terms in an equation with any number and it will not change the solutions to the equation.

You can exploit this property while solving simultaneous equations.

You should multiply one of the equations by a number which will produce the opposite coefficient for one of the variables, thereby eliminating it, allowing you to proceed with one equation in one variable, which is easily solvable.

By multiplying the first equation by \(2\), you can get rid of the \(y\)-term, enabling you to solve for the \(x\)-term
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If -5x + 2y = 9 and 3x - 4y = -4, then what is the value of 7x + 10y ? [#permalink]
07 Apr 2023, 22:31
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