Solve.
{d+e=2d−e=4
use the substitution method.

there are an infinite number of solutions.
there is no solution.
the solution is (3, −1).
the solution is (5, 1).

Option  C is correct.

The solution is (3, -1)

Step-by-step explanation:

Substitution

Given the system of equation:

                           ......[1]

                            ......[2]

We can write equation [2] as;

d = e +4       ....[3]

Using substitution method;

Substitute the value of d in equation [1] we have;

Combine like terms;

Subtract 4 from both sides, we get

2e = -2

Divide both sides by 2 we get;

e = -1

Substitute the value of e = -1 in [1] we have;

d +(-1) = 2

d -1 = 2

Add 1 to both sides of an equation;

d = 3

Therefore, the solution for the given system of equation is, (3, -1)

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°

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?