2x- 3y = -2 ,4x+y = 24 by cross multiplication
Answers
Step-by-step explanation:
2x-3y=-2
2x=-2+3y
x=3y-2/2
4x+y=24
4(3y-2/2)+y=24
6y-4+y=24
7y=28
y=28/7=4
x= 3y-2/2
x=3×4-2/2
x=10/2
x=5
Answer:
x=
47
5
and y=−
47
23
Step-by-step explanation:
\boxed{\huge{\bf{\pink{Answer}}}}
Answer
x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47}x=
47
5
and y=−
47
23
Step-by-step explanation:
\begin{gathered}Given \ 5x-3y=2 \ and \ 4x+7y=-3\\\\\end{gathered}
Given 5x−3y=2 and 4x+7y=−3
We have to find the value of x and y by using cross multiplication method.
\begin{gathered}For \ cross \ multiplication \ method \ we \ have\\\\\dfrac{x}{b_1c_2-b_2c_1}=\dfrac{y}{c_1a_2-c_2a_1}=\dfrac{1}{a_1b_2-a_2b_1}\\\\\\5x-3y-2=0 \ and \ 4x+7y+3=0\\\\\\we \ have\\\\a_1=5 \ b_1=-3 \ and \ c_1=-2\\\\\\a_2=4 \ b_2=7 \ and \ c_2=3\\\\\\putting \ value \ in \ formula\end{gathered}
For cross multiplication method we have
b
1
c
2
−b
2
c
1
x
=
c
1
a
2
−c
2
a
1
y
=
a
1
b
2
−a
2
b
1
1
5x−3y−2=0 and 4x+7y+3=0
we have
a
1
=5 b
1
=−3 and c
1
=−2
a
2
=4 b
2
=7 and c
2
=3
putting value in formula
\begin{gathered}\dfrac{x}{(-3\times3)-(7\times-2)}=\dfrac{y}{(-2\times4)-(3\times5)}=\dfrac{1}{(5\times7)-(4\times-3)}\\\\\\ \dfrac{x}{-9+14}= \dfrac{1}{35+12} \ and \ \dfrac{y}{-8-15}= \dfrac{1}{35+12}\\\\\\x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47}\end{gathered}
(−3×3)−(7×−2)
x
=
(−2×4)−(3×5)
y
=
(5×7)−(4×−3)
1
−9+14
x
=
35+12
1
and
−8−15
y
=
35+12
1
x=
47
5
and y=−
47
23
So we get our answer
x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47}x=
47
5
and y=−
47
23
\begin{gathered}Verification\\\\\\putting \ x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47} \ in \ 5x-3y=2\\\\\\\L.H.S.=(5\times\dfrac{5}{47})-3\times(-\dfrac{23}{47})\\\\\\L.H.S.=\dfrac{25+69}{47}=2\\\\\\L.H.S.=R.H.S\\\\Now \ putting \ in \ 4x+7y=-3\\\\\\L.H.S.=(4\times\dfrac{5}{47})+(7\times-\dfrac{23}{47})\\\\\\L.H.S.=\dfrac{20-161}{47}\\\\\\L.H.S=\dfrac{-141}{47}=-3\\\\\\L.H.S.=R.H.S\\\\\\Hence \ we \ verified \ it.\end{gathered}
Verification
putting x=
47
5
and y=−
47
23
in 5x−3y=2
\L.H.S.=(5×
47
5
)−3×(−
47
23
)
L.H.S.=
47
25+69
=2
L.H.S.=R.H.S
Now putting in 4x+7y=−3
L.H.S.=(4×
47
5
)+(7×−
47
23
)
L.H.S.=
47
20−161
L.H.S=
47
−141
=−3
L.H.S.=R.H.S
Hence we verified it.