Question

Solve the following equations by the substitution method

$x=3y-19,y=3x-23$

• A. $x=5,y=7$
• B. $x=11,y=10$
• C. $x=13,y=7$
• D. $x=3,y=11$

Answer 1

The correct option is B $x=11,y=10$

The equations are
$\Rightarrow x=3y-\mathrm{19....}eq\left(1\right)$
$\Rightarrow y=3x-\mathrm{23....}eq\left(2\right)$
Substitute the value of x in eq (2 )
$\Rightarrow y=3(3y-19)-23$
$\Rightarrow y=9y-57-23\Rightarrow -8y=-80\Rightarrow y=10$
Substitute the value of y in eq (1 )
$\Rightarrow x=3\left(10\right)-19\Rightarrow x=30-19\Rightarrow x=11$
$\Rightarrow x=11,y=10$