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| 1. |
S+t=3;S/4+t/3=6;Solve the following pair of equation |
| Answer» s - t = 3;\xa0{tex}\\frac { s } { 3 } + \\frac { t } { 2 } = 6{/tex}The given pair of linear equations is :s - t = 3...............(1){tex}\\frac { s } { 3 } + \\frac { t } { 2 } = 6{/tex}..........(2)From equation(1),s = t + 3..............(3)Substitute this value of s in equation(2), we get{tex}\\frac { t + 3 } { 3 } + \\frac { t } { 2 } = 6{/tex}{tex}\\Rightarrow \\quad \\frac { 2 ( t + 3 ) + 3 t } { 6 } = 6{/tex}{tex}\\Rightarrow {/tex}2(t + 3) + 3t = 36{tex}\\Rightarrow {/tex}\xa02t + 6 + 3t = 36{tex}\\Rightarrow {/tex}\xa05t + 6 = 36{tex}\\Rightarrow {/tex}\xa05t = 30{tex}\\Rightarrow \\quad t = \\frac { 30 } { 5 } = 6{/tex}Substituting this value of t in equation (3), we gets = 6 + 3= 9therefore the solution is\xa0s = 9, t = 6Verification : Substituting s = 9 and t = 6, we find that both equation (1) and (2) are satisfied as shown below:s - t = 9 - 6 = 3{tex}\\frac { s } { 3 } + \\frac { t } { 2 } = \\frac { 9 } { 3 } + \\frac { 6 } { 2 } = 3 + 3 = 6{/tex}This verifies the solution. | |