Question

How do you solve 7x+y=11 and 3x+2y=−11 using substitution?

Answer 1

Answer :

$7x + \: \: y = \: \: \: 11 \: ......(i)\\ 3x + 2y = - 11.......(ii)$

Solving the eqⁿ (i)

$7x + y = 11 \\ \\ y = 11 - 7x$

Put the value of y in (ii),

$3x + 2y = - 11 \\ \\ 3x + 2( 11 - 7x) = - 11 \\ \\ 3x + 22 - 14x + 11 = 0 \\ \\ - 11x + 33 = 0 \\ \\ 11x = 33 \\ \\ x = \frac{33}{11} \\ \\ \boxed{ \fcolorbox {red}{yellow}{ \bf x = 3}}$

Substituting the value of x in (i),

$7x + y = 11 \\ \\ 7 \times 3 + y = 11 \\ \\ 21 + y = 11 \\ \\ y = 11 - 21 \\ \\ \boxed{ \fcolorbox{red}{yellow}{ y = - 10}}$

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