Solving pairs of equations, indicate the pair or pairs representing simultaneous linear equations (solvable).
1. From the following pairs of equations find the pair or pairs representing simultaneous equations:
(i) 7x – 3y = 5
2x + 5y = 1
Solution:
7/2 ≠ -3/5, so the two equations represent simultaneous equations; in this case they have only one solution.
(ii) 2x + 3y = 7
6x + 9y = 11
Solution:
2/6 = 3/9 ≠ 7/11
Not simultaneous equations.
(iii) 6x - 4y = 8
3x - 2y = 4
Solution:
6/3 = -4/-2 = 8/4
Simultaneous equations; have infinite solutions.
2. For which value of k, kx + y = 2 and x + ky = 1 are inconsistent?
Solution:
The two equations will be inconsistent if k/1 = 1/k ≠ 2/1 that means, k² = 1 or k = ±1
Therefore, the two given equations will be inconsistent if k = ±1
3. If solvable, solve the following pairs of equations:
(i) 3x – 2y = 1
3x + 2y = 5
Solution:
Here, comparing co-efficient of x and y, we get;
3/3 ≠ -2/2
Therefore, adding the two equations, we get the general solution as shown below:
6x = 6
or, x = 1
Putting x = 1 in the first equation we get:;
3 × 1 – 2y = 1
or, 3 - 2y = 1
or, 3 – 3 – 2y = 1 – 3
or, -2y = -2
or, y = 1
Therefore, the required solution: x = 1, y = 1
(ii) 3x – 2y = 1
6x – 4y = 8
Solution:
Here, comparing the co-efficient of x, y we get;
3/6 = -2/-4 ≠ 1/8
So, the two equations have no general solution.
(iii) 3x – 2y = 2
9x – 6y = 6
Solution:
Comparing co-efficient of x, y and the term free from x, y we get;
3/9 = -2/-6 = 2/6
Therefore, two equations are, in fact, same.
Assuming x = c in 3x – 2y = 2 we get;
y = (3c – 2)/2
Therefore, required solution: x = c
y = (3c – 2)/2 for any real value of c.
● Simultaneous Linear Equations
Solvability of Linear Simultaneous Equations
Word Problems on Simultaneous Linear Equations
Word Problems on Simultaneous Linear Equations
Practice Test on Word Problems Involving Simultaneous Linear Equations
● Simultaneous Linear Equations - Worksheets
Worksheet on Simultaneous Linear Equations
Worksheet on Problems on Simultaneous Linear Equations
8th Grade Math Practice
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