Answer:
(a) No solution
(b) Infinitely many solution
(c) No solution
(d) Infinitely many solution
Step-by-step explanation:
Solving (a):
[tex]2x + 10y = 9[/tex] --- (1)
[tex]3x + 15y = 13[/tex] --- (2)
Multiply (1) by 1.5
1.5 * [[tex]2x + 10y = 9[/tex]]
[tex]3x + 15y = 13.5[/tex] --- (3)
Subtract 2 and 3
[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]
[tex]0 = 0.5[/tex]
The above is false; Hence, the system has no solution
Solving (b):
[tex]2x + 8y = 5[/tex] --- (1)
[tex]3x + 12y = 7.5[/tex] -- (2)
Multiply 1 by 1.5
1.5 * [[tex]2x + 8y = 5[/tex]]
[tex]3x + 12y = 7.5[/tex]
Subtract 2 and 3
[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Solving (c):
[tex]y = 3 - x[/tex]
A second equation is required to solve for (c)
Solving (d):
[tex]5x - 8y = -1[/tex] --- (1)
[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)
Multiply (2) by 2
[tex]-5x + 8y = 1[/tex] --- (3)
Add 1 and 3
[tex]5x - 5x -8y + 8y = -1 + 1[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
