Question
Solve the following simultaneous equations by the substitution method:$x + 3y= 5,7x - 8y = 6$
✓
Answer
The given equations are
$x + 3y= 5 \dots....(i)$
$7x - 8y = 6\dots ....(ii)$
Now, consider equation
$x + 3y = 5$
$\Rightarrow x = 5 - 3y \dots....(iii)$
Substituting the value of $x$ in eqn. $(ii)$, we get
$7(5 - 3y) - 8y = 6$
$\Rightarrow 35 - 21y - 8y = 6$
$\Rightarrow 35 - 29y = 6$
$\Rightarrow -29y = -29$
$\Rightarrow y = 1$
Putting the value of $y$ in eqn.$ (ii),$ we get
$x = 5 - 3(1)$
$= 5 - 3 = 2$
Thus, the solution set is$ (2, 1).$
$x + 3y= 5 \dots....(i)$
$7x - 8y = 6\dots ....(ii)$
Now, consider equation
$x + 3y = 5$
$\Rightarrow x = 5 - 3y \dots....(iii)$
Substituting the value of $x$ in eqn. $(ii)$, we get
$7(5 - 3y) - 8y = 6$
$\Rightarrow 35 - 21y - 8y = 6$
$\Rightarrow 35 - 29y = 6$
$\Rightarrow -29y = -29$
$\Rightarrow y = 1$
Putting the value of $y$ in eqn.$ (ii),$ we get
$x = 5 - 3(1)$
$= 5 - 3 = 2$
Thus, the solution set is$ (2, 1).$
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