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3 years ago

X+y=4 and 2x+3y=2 then find x and y

Mathematics

1 answer:

Sladkaya [172]3 years ago

8 0

Answer:

x=10, y=-6

Step-by-step explanation:

1) express x from the first equation x+y=4 x=4-y

2) It is the system of equations, so both equations are simultaneous.

you can replace x to 4-y in the second one

2 *(4-y) +3y=2

8-2y+3y= 2

y=-6

x= 4-y=4-(-6)=10

The answer is x=10, y=-6

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Find the coordinates of point which divides the line segment joining the points (a+b,a-b) and (a-b,a+b) in the ratio 3:2 interal

sasho [114]

Answer:

Coordinate of 0 = $\bigg( \dfrac{5a-b}{5},\:\dfrac{5a+b}{5}\bigg)$

Step-by-step explanation:

Let AOB be the line segment
Point 'O' divides the line segment into m:n = 3:2

Given:

Coordinate of a = (a+b, a-b)
Coordinate of b = (a-b, a+b)
Ratio = 3:2

ToFind:

Coordinate of 0 (zero)

Solution:

ATQ,

$\dfrac{m}{n}=\dfrac{3}{2}$
Coordinate of a = (x $_{1}$ , y $_{1}$ )
Coordinate of b = (x $_{2}$ , y $_{2}$ )

As we know that,

$\implies\:\:x = \dfrac{mx_{2} + nx_{1}}{m + n}$

$\implies\:\:x = \dfrac{(a-b)3 + (a+b)2}{3+2}$

$\implies\:\:x = \dfrac{3a - 3b + 2a + 2b}{5}$

$\implies\:\:\red{x = \dfrac{5a - b}{5}}$

Similarly,

$\implies\:\:y = \dfrac{my_{2}+ny_{1}}{m+n}$

$\implies\:\:y = \dfrac{(a+b)3+(a-b)2}{3+2}$

$\implies\:\:y = \dfrac{3a+3b+2a-2b}{5}$

$\implies\:\:\red{y = \dfrac{5a+b}{5}}$

Hence,

Coordinate of 0 is $\blue{\bigg( \dfrac{5a-b}{5},\:\dfrac{5a+b}{5}\bigg)}$

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X+y=4 and 2x+3y=2 then find x and y​

X+y=4 and 2x+3y=2 then find x and y