Solve the system. -0.18x + y = -6.54 -2.8x - y = -2.4 A) (8, 8) B) (3, -6) C) (-6, 5.46) D) (-3, -22.8)

x = 3 , y = -6 thus B is the Answer

Step-by-step explanation:

Solve the following system:

{y - 0.18 x = -6.54

{-2.8 x - y = -2.4

In the first equation, look to solve for y:

{y - 0.18 x = -6.54

{-2.8 x - y = -2.4

y - 0.18 x = y - (9 x)/50 and -6.54 = -327/50:

y - (9 x)/50 = -327/50

Add (9 x)/50 to both sides:

{y = 3/50 (3 x - 109)

{-2.8 x - y = -2.4

Substitute y = 3/50 (3 x - 109) into the second equation:

{y = 3/50 (3 x - 109)

{-2.8 x - 3/50 (3 x - 109) = -2.4

-2.8 x - (3 (3 x - 109))/50 = (327/50 - (9 x)/50) - 2.8 x = 327/50 - 2.98 x:

{y = 3/50 (3 x - 109)

327/50 - 2.98 x = -2.4

In the second equation, look to solve for x:

{y = 3/50 (3 x - 109)

327/50 - 2.98 x = -2.4

327/50 - 2.98 x = 327/50 - (149 x)/50 and -2.4 = -12/5:

327/50 - (149 x)/50 = -12/5

Subtract 327/50 from both sides:

{y = 3/50 (3 x - 109)

{-(149 x)/50 = -447/50

Multiply both sides by -50/149:

{y = 3/50 (3 x - 109)

x = 3

Substitute x = 3 into the first equation:

{y = -6

{x = 3

Collect results in alphabetical order:

{x = 3 , y = -6

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!