Question

Solve for 'x' and 'y', using the method of substitution:
4x + 3y = 12; x - 6y = 9

• A. $x=-\frac{33}{9},y=\frac{8}{9}$
• B. $x=\frac{9}{33},y=-\frac{9}{33}$
• C. $x=-\frac{8}{9},y=\frac{33}{9}$
• D. $x=\frac{33}{9},y=-\frac{8}{9}$

Answer 1

The correct option is D $x=\frac{33}{9},y=-\frac{8}{9}$

$4x+3y=12$ ___(i)
$x-6y=9$ _____(ii)
From equation (ii),
$x=6y+9$ _____(iii)
Plug this value in equation (i)
$⟹4(6y+9)+3y=12$
$24y+36+3y=12$
$27y=-24$
$y=-\frac{8}{9}$
Plug the value of y in equation (iii): $x=6y+9$
$x=-\frac{48}{9}+9$
$x=\frac{33}{9}$
The solution is $\frac{33}{9},-\frac{8}{9}$