System of equations | Solutions |
(P) \[2x-3y+15=0\] \[3x-5=0\] | (i) \[x=3,\text{ }y=5\] |
(Q) \[2x-y=1\] \[4x+3y=27\] | (ii) \[x=1,y=4\] |
(R) \[x+2y-3=0\] \[3x-2y+7=0\] | (iii) \[x=\frac{5}{3},y=\frac{55}{9}\] |
(S) \[4x+\frac{y}{3}=\frac{16}{3}\] \[\frac{x}{2}+\frac{2y}{4}=\frac{5}{2}\] | (iv) \[x=-1,y=2\] |
(i) If pair of linear equations is consistent then it has either P or Q solution(s). |
(ii) If the pair of linear equation is inconsistent then it has B solution(s). |
(iii) If the graph of two linear equations coincide then they have S solution(s). |
P | Q | R | S |
no | Infinite | Unique | Infinite |
P | Q | R | S |
unique | Infinite | No | Infinite |
P | Q | R | S |
no | Infinite | Unique | Unique |
P | Q | R | S |
unique | No | Infinite | No |
(i) The pair of linear equations \[x+2y=5\]and \[7x+3y=13\] has unique solution\[x=2.\text{ }y=1\]. |
(ii) \[\sqrt{2}x+\sqrt{3}y=0,\] \[\sqrt{3}x-\sqrt{8}y=0\] has no solution. |
(iii) The values of p and q for which the following system of equations \[2x-y=5,\] \[(p+q)x+(2p-q)y=15\]has infinite number of solutions, is \[p=1\]and\[q=5\]. |
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