Question

solve the following system of equations.\
$0.4x - 0.2y = 5$\
$0.7x - 0.6y = 11$\
$x = \square$\
$y = \square$

Explanation:

Step1: Eliminate decimals, scale eq1

Multiply first equation by 10:
$4x - 2y = 50$

Step2: Eliminate decimals, scale eq2

Multiply second equation by 10:
$7x - 6y = 110$

Step3: Scale eq1 for y elimination

Multiply scaled eq1 by 3:
$12x - 6y = 150$

Step4: Subtract eq2 from new eq1

Eliminate $y$ to solve for $x$:
$(12x - 6y) - (7x - 6y) = 150 - 110$
$5x = 40$
$x = 8$

Step5: Substitute x into scaled eq1

Solve for $y$ using $4x - 2y = 50$:
$4(8) - 2y = 50$
$32 - 2y = 50$
$-2y = 18$
$y = -9$

Answer:

$x = 8$
$y = -9$