EXERCISE-A
1) x+ y=7; y+3= x. 5, 2
2) x+ y -5= 0; y- 2x= 9.
3) x+2y -1= 0; 3x- y -17= 0. 5, -2
4) y= x, x+ 2y= 0.
5) x -2y+9=0; 3x+4y+17= 0. 1,-5
6) x - 2y= 1, x+ y= 4. 3,1
7) x- 5y+4= 0; 3x-5y+1= 0
8) x+ y=3, 2x+5y= 12
9) x+y= 4, 3x - 2y= 7.
10) x +3y= 8, 3x= 2+ 2y
11) x + y= -1, y - 2x= -4
12) x + 6y= 11, 2x -3y= 7
13) x + 2y= 7, 2x- y +1= 0
14) x +y +3= 0, 3x - 2y +4= 0
15) x + y +2=0 , 3x -4y= 15.
16) x+ 2y+1= 0, 2x-3y-12= 0. 3, -2
EXERCISE - B
1) 2x= y +3, 3y= 5 - x.
2) 2x +y= 8, x+1= 2y
3) 2x- y -1= 0, 2x+y= 9
4) 2x + 5y= -1, 3x - y= 7
5) 2x- 3y= 7, x+y= 1
6) 2x- 3y= 6, 2x+y= -10.
7) 2x- y +4= 0, 3x+ 2y-1= 0
8) 2x+y= 3; x - 3y = -2. 1,1
9) 2x+ 3y=11, x-2y= 2. 4,1
10 2x + y= 7, 4x - 3y +1= 0. 2, 3
11) 2x+3y=23; 5x-20= 8y.
12) 2x+ y= 35, 3x+4y= 65. 15, 5
13) 2x- y= 6, x-y= 2. 4, 2
14) 2y- x= 8, 5y - x= 14.
15) 2y - x= 8, y - 2x = 1.
EXERCISE - C
1) 3x- 5y +18= 0, 3x+ 5y= 12
2) 3x- 5y +1= 0, 2x-y +3= 0
3) 3x+7y=15; 5x-129= 23y. 12,-3
4) 3x+2y=11; x- y= 3.
5) 3x+2y= 0; 5x+2y= 9.
6) 3x-5y+1=0, 2x- y+3= 0. -2,-1
7) 3x+2y +25= 0, 2x+y+10= 0. 5, -20
8) 3x -y= 23; 4x+ 3y= 48. 9,4
9) 4x- 5y= -4, 3x= 2y -3
10) 4x - y=10; 2x+3y= 11.
11) 4x- 18= 3y; 6x+7y= 4. 3,2
EXERCISE - D
1) 5x- y= 15, 5x - 6y +10= 0
2) 5y - x= 14, y - 2x = 1
3) 5x- 8y= -4, 2x- 7y= 6
4) 5x+ 4y-4= 0, x-20= 12y. 2, -3/2
) 10x + 3y = 75, 6x - 5y= 11. 6,5
) 11x + 15y +23 = 0, 7x - 2y -20 = 0.
) 0.4x - 1.5y= 6.5; 0.3x + 0.2y= 0.9. 5,-3
EXERCISE --3
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1) 5/x + 6y =13, 3/x + 4y= 7. 1/5, -2
2) 2x-3y/4=3, 5x = 2y+7. 3,4
3) x -2y/3= 8/3, 2x/5 - y= 7/5. 26/11, -5/11
4) x/6 + 6= y, 3x/4 = 1+ y. 12,8
5) x/2 + y= 0.8, 7/(x + y/2)= 10. 2/5, 3/5
6) 4x + 6/y= 15, 3x - 4/y= 7. 3, 2
7) 3x/5 - 2y +1= 0; 2x/5 + y/3 -4= 0. 5, 6
8) x/7 + y/3= 5, x/2 - y/9= 6. 14,9
9) x/3 + y/4= 11, 5x/6 - y/3 +7= 0. 6, 35
10) 1/7x + 1/6y= 3, 1/2x - 1/3y = 5. 1/14, 1/6
11) 2/x + 2/3y= 1/6, 3/x + 2/y = 0. 6, -4
12) 3/2x + 2/3y= 5, 5/x - 3/y = 1. 1/2, 1/3
) 3x/2 - 5y/3 = -2, x/3+ y/2= 13/6. 2,3
) 4/x + 3y= 8; 6/x - 4y = -5. 2,2
) 2/x + 3/y= 13; 5/x - 4/y = -2. 1/2, 1/3
) 1/2x - 1/y = -1; 1/x + 1/2y = 8 (x≠ 0, y ≠0).
) 1/7x + 1/6y = 3 ; 1/2x - 1/3y = 5 (x≠ 0, y ≠0). 1/14,1/6
) 3a/x - 2b/y = - 5 ; a/x + 3b/y -2 = 0 (x≠ 0, y ≠0).
EXERCISE--4
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1) 5x -9= 1/y, x + 1/y = 3. 2, 1
2) x+ y= 2xy, x- y= 6xy. -1/2, 1/4
3) 3x+ 2y= 2xy, 6x +2y= 3xy. 2, 3
4) (x+y)/xy = 2, (x-y)/xy = 6. 15, 5
5) 2/x + 3/y = 13, 5/x - 4/y =-2. 1/2, 1/3
6)
EXERCISE -5
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1) ax+ by= a- b; bx - ay= a+ b. (a²+ab+b²/(a+b), -ab/(a+b)
2) x+ ay= b, ax- by = c. (ac+b²)/(a²+b), (ab-c)/(a²+b)
3) x/a + y/b = 2; ax - by = a² - b². a, b
4) x/a + y/b = a+ b; x/a² + y/b²= 2. a², b²
5) x/a = y/b, ax + by= a²+ b². a, b
6) ax + by= (a+b)/2; 3x + 5y = 4. 1/2, 1/2
7) 2ax + 3by= a+ 2b; 3ax + 2by= 2a+ b;
8) 5ax + 6by= 28; 3ax + 4by= 18. 2/a, 3/b
)
EXERCISE -6
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1) 5/(x+y) - 2/(x-y)= -1
15/(x+y) + 7/(x-y)= 10. 3,2
2) 57/(x+y) + 6/(x - y) = 5
38/(x +y) + 7/(x- y) = 9. 11, 8
Harder problem
1) x{a - b +ab/(a-b)}= y{a+b - ab/(a+b)}, x+ y= 2a². (a³-b³)/a, (a³ + b³)/a.
2) bx + cy = a+ b,
ax{1/(a-b) - 1/(a+b)} + cy{1/(b-a) - 1/(a+b)}= 2a/(a+b). a/b, b/c
3) (a-b)x + (a+b)y= 2a² -2b²;
(a +b) (x+y)= 4ab. (2ab -a²+ b²)/b, {(a-b)(a²+ b²)}/{b(a+b)}
4) (a+ 2b)x + (2a-b) y= 2
(a- 2b)x + (2a+ b) y= 3. (5b-2a)/10ab, (a + 10b)/10ab
5) a²x + b²y= c²; b²x + a²y= d². (a²c²- b²d²)/(a⁴- b⁴), (a²d²- b²c²)/(a⁴- b⁴)
6) 2(ax- by) + a + 4b= 0;
2(bx- ay) + b - 4a= 0. 1/2,1/3
7) 6(ax+ by) = 3a + 2b
6(bx- ay) = 3b - 2a
MISCELLANEOUS EXERCISE
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