(08.01)consider the following system of equations:
y = −x + 2
y = 3x + 1
which description best describes the solution to the system of equations?
line y = −x + 2 intersects line y = 3x + 1.
lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
line y = −x + 2 intersects the origin.

Line y = −x + 2 intersects line y = 3x + 1

Step-by-step explanation:

we have

y=-x+2 > equation A

y=3x+1 > equation B

we know that

The solution of the system of equations is the intersection point both graphs

The slope of Line A (m=-1) is different to the slope of Line B (m=3)

so

The system of equations A and B has only one solution

This is a consistent independent system  

therefore

The description that best describes the solution  to the system of equations is

Line y = −x + 2 intersects line y = 3x + 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°