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Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5

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Bunuel
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Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 [#permalink] New post   19 Oct 2021, 05:30
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Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 intersect?

(A) (3, –5)
(B) (1,0)
(C) (2/3,-7)
(D) (29/19,-50/19)
(E) The two lines are parallel; they don't intersect.
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sallyvn
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Re: Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 [#permalink] New post   19 Oct 2021, 07:54
5x + 2y =5 => y = (5-5x)/2
(5-5x)/2 = 2x/3 − 7 => x = 3. Substitute the x value in one of the line equations y = -5
=>A
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Re: Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 [#permalink] New post   19 Oct 2021, 11:45
Bunuel wrote:
Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 intersect?

(A) (3, –5)
(B) (1,0)
(C) (2/3,-7)
(D) (29/19,-50/19)
(E) The two lines are parallel; they don't intersect.

\(y = \frac{2x}{3} − 7\)

Or, \(3y = 2x - 21\)

Or, \(6y = 4x - 42\)--------------------(I)

\(5x + 2y =5\)

Or, \(15x + 6y = 15\)--------------------(II)

Now, substitute \(6y\)

Or, \(4x - 42 = 15 - 15x\)

So, \(19x = 57\)

Or, \(x = 3\), Check the given options only (A) satisfies, Answer must be (A)
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shalin23
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Re: Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 [#permalink] New post   11 Nov 2021, 05:39
One easy way is to substitute the value from the options given.

Both the equation should satisfy the value pair provided; meaning, when I put x=3 in both equations, I get y =-5 and correspondingly I put y=-5, I get x=3 for both equations.

Hence option A is the right answer choice.
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Re: Where in the coordinate plane do the lines y = 2x/3 − 7 and 5x + 2y =5 [#permalink]
11 Nov 2021, 05:39
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