A linear equation is a mathematical expression that depicts a straight line within a twodimensional Cartesian coordinate system. This equation is commonly expressed in the form y=mx+b.
Here are some useful tips to help you solve linear equations efficiently:
Example 1: The roots of the equation 4x − 3 × 2x + 2 + 32 = 0 would include
(a) 20
(b) 40
(c) 5
(d) 17
Ans: (d)
4x−3×2x+2+32=0
4x−6x+34=0
−2x+34=0
2x−34=0
2x=34
x=17
Example 2: If x = 1+21/2 and y=121/2, then x^{2 }+ y^{2} is 
(a) 107/2
(b) 203/2
(c) 997/2
(d) 445/2
Ans: (d)
x = 1+21/2 and y=121/2
x^{2}+ y^{2}
2 + 441/2
445/2
Example 3: 2x+y=2 and 2x  y = 21/2 ,the value of x is:
(a) 10/14
(b) 9/8
(c) 25/8
(d) 5/4
Ans: (c)
2x + y = 2
2x  y = 21/2
Adding both equations we get:
4x = 25/2
x = 25/8
Putting this in
Example 4: What is the slope of the line represented by the equation 3y+4x=12?
(a) 3/4
(b) −4/3
(c) 3
(d) −4
Ans: (b)
To find the slope of the line, we need to rewrite the equation in slopeintercept form (y=mx+b), where m is the slope.
Solving for y gives
The coefficient of x represents the slope, so the correct answer is −4/3
Example 5: If 6(x3) = 36(x5), then what is the value of x?
(a) 51/5
(b) 27/5
(c) 15/7
(d) 17/3
Ans: (b)
6(x3) = 36(x5)
x  3 = 6(x  5)
x  3 = 6x  30
5x = 27
x = 27/5
Example 6: If ax = b, by = c and cz = a, then the value of xyz is:
(a) 4
(b) 3
(c) 2
(d) 1
Ans: (d)
ax = b, by = c and cz = a
x = b/a
y = c/b
z = a/c
xyz = 1
Example 7: If 4x + 3 = 2x + 7, then the value of x is:
(a) 2
(b) 3
(c) 1
(d) 4
Ans: (a)
4x+3 = 2x+7
2x = 4
x = 2
Example 8: If x = 8, y = 27, the value of
(a)
(b)
(c)
(d)
Ans: (b)
Example 9: If 2x + 3y = 16 and 2x  3y= 36, the value of x is:
(a) 13
(b) 23
(c) 33
(d) 43
Ans: (a)
2x + 3y = 16 (1)
2x  3y= 36  (2)
adding both eq we get
4x = 52
x = 13
Example 10: Determine whether the ordered triple (3,−2,1) is a solution to the system.
2x+y+z=5,
6x−4y+5z=31,
5x+2y+2z=13
(a) True
(b) False
(c) No solution
(d) None of the above
Ans: (a)
We will check each equation by substituting the values of the ordered triple for x,y, and z
x+y+z=2(3)+(−2)+(1)=5 True
6x−4y+5z=6(3)−4(−2)+5(1)=18+8+5=31 True 5x+2y+2z=5(3)+2(−2)+2(1)=15−4+2=13 True
The ordered triple (3,−2,1) is indeed a solution to the system.
314 videos170 docs185 tests

314 videos170 docs185 tests


Explore Courses for SSC CGL exam
