How do you solve $2 X - 3 Y = 21$ $2X-3Y=21$ and $5 X + 4 Y = - 5$ $5X+4Y=-5$ ?

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How do you solve $2 X - 3 Y = 21$ $2X-3Y=21$ and $5 X + 4 Y = - 5$ $5X+4Y=-5$ ?

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Answer 1 · 2018-04-13T03:31:04

Nithish B.

Apr 13, 2018

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Answer 2 · 2018-04-13T03:36:18

(3,-5)

Explanation:

I'm going to assume you are looking for the intersection of the two.
Lets start by solving both for y.
$2 X - 3 Y = 21$ $2X-3Y=21$ , therefore $3 Y = 2 X - 21$ $3Y = 2X-21$ , and $Y = \frac{2 X - 21}{3}$ $Y = (2X-21)/3$
$5 X + 4 Y = - 5$ $5X+4Y=-5$ , $4 Y = - 5 X - 5$ $4Y=-5X-5$ and $Y = - \frac{5}{4} (X + 5)$ $Y = -5/4(X+5)$
Now lets try seeing for what value of x, these two equations are equal (and therefore Y=Y)
$Y = Y, \frac{2 X - 21}{3} = - \frac{5}{4} (X + 1)$ $Y=Y, (2X-21)/3 = -5/4(X+1)$
$4 (2 X - 21) = - 15 (X + 1)$ $4(2X-21)=-15(X+1)$
$4 (2 X - 21) + 15 (X + 1) = 0$ $4(2X-21)+15(X+1)=0$
$8 X - 84 + 15 X + 15 = 0$ $8X-84+15X+15=0$
$23 X - 69 = 0$ $23X-69=0$
And finally,
$X = 3$ $X=3$
Now, lets find the value of y but inserting this x into either of the original equations!
$2 X - 3 Y = 21$ $2X-3Y=21$
$2 (3) - 3 Y = 21$ $2(3)-3Y=21$
$6 - 3 Y = 21$ $6-3Y=21$
$3 Y = - 15$ $3Y=-15$
$Y = - 5$ $Y=-5$
Therefore, the answer is (X,Y)=(3,-5)

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How do you solve $2 X - 3 Y = 21$ $2X-3Y=21$ and $5 X + 4 Y = - 5$ $5X+4Y=-5$ ?

2 Answers

Explanation:

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