solve the simultaneous equations 3x-5y=4 & 9x-2y=7
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Answers
Answer:
(i) We have, 3x−5y−4=0
⇒3x−5y=4...(i)
Again 9x=2y+7
⇒9x−2y=7...(ii)
By Elimination Method:
Multiplying equation (i) by 3, we get
9x−15y=12...(iii)
Subtracting (ii) from (iii), we get
9x−15y=12
9x−2y=7
−13y=5
⇒y=−
13
5
Putting the value of equation (ii), we get
9x−2(−
13
5
)=7
⇒9x+
13
10
=7
⇒9x=7−
13
10
⇒9x=
13
91−10
⇒9x=
13
81
⇒x=
13
9
Hence, the required solution is x=
13
9
,y=−
13
5
By Substitution Method:
Expressing x in terms of y from equation (i), we have
x=
3
4+5y
Substituting the value of x in equation (ii), we get
9×(
3
4+5y
)−2y=7
⇒3×(4+5y)−2y=7
⇒12+15y−2y=7
⇒13y=7−12
∴y=−
13
5
Putting the value of y in equation (i), we have
3x−5×(−
13
5
)=4
⇒3x+
13
25
=4
⇒3x=4−
13
25
⇒3x=
13
27
∴x=
13
9
Hence, the required solution is x=
13
9
, y=−
13
5
.
(ii) We have,
2
x
+
2
2y
=−1
⇒
6
3x+4y
=−1
∴3x+4y=−6...(i)
And x−
2
y
=3⇒
3
3x−y
=3
∴3x−y=9...(ii)
By Elimination Method:
Subtracting (ii) from (i), we get
5y=−15 ⇒y=−
5
15
=−3
Putting the value of y in equation (i), we get
3x+r×(−3)=−6
⇒3x−12=−6
⇒3x=−6+12⇒3x=6
Hence, Solution is x=2 , y=−3
By Substitution Method:
Expressing x in terms of y from equation (i), we have
x=
3
−6−4y
Substituting the value of x in equation (ii) from equation (i), we get
3×(
3
−6−4y
)−y=9
⇒−6−4y−y=9
⇒−6−5y=9
⇒−5y=9+6=15
∴y=
−5
15
=−3
Putting the value of y in equation (i), we get
3x+×(−3)=−6
⇒3x−12=−6
⇒3x=12−6=6
∴x=
3
6
=2
Hence, the required solution is x=2,y=−3
Step-by-step explanation:
༆ ɑnswer ࿐
9 } Sol :— Given that
P (x) = 6x³ + 13x² + 3
g (x) = 3x + 2 = 0
:— 3x = 0 –2
3x = —2
x = —2/3
so, x = —2/3
put the value ...
p (—2/3) = 6 x (—2/3)³ + 13 x (—2/3)² + 3
= 6x —8/27 + 13 x 4/9 + 3
= —16/9 + 52/9 + 3/1
we will take LCM got = 9
= —16+52+27 / 9
= —16+79 / 9
= 63/8 Sol :— 7 Ans...
11 } Sol :— p(x) = 2x³+3x²—11x—3
g(x) = x + 1/2
:— x = —1/2
put the value ...
p(—1/2) = 2x (—1/2)³+ 3x (—1/2)²—11x (—1/2) —3
= 2x (—1/8) + 3x (1/4) —11x (—1/2) —3
= 2 x—1/8 + 3/4 — (—11) /2 —3
= —1/4 + 3/4 + 11/2 —3/1
we will take LCM got = 4
= —1 +3 +22 —12 / 4
= —1 +25 —12 / 4
= 24 — 12 / 4
= 12 / 4 Sol :— 3 Ans...
Hope it may help you...
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