Which description best describes the solution to the following system of equations?

y = −x + 4
y = 3x + 3

line y = −x + 4 intersects the line y = 3x + 3.
lines y = −x + 4 and y = 3x + 3 intersect the x-axis.
lines y = −x + 4 and y = 3x + 3 intersect the y-axis.
line y = −x + 4 intersects the origin.

Line y = −x + 4 intersects the line y = 3x + 3.

Step-by-step explanation:

The given system of equations is

In graphical method of solving linear system of equations, we plot the graph of the given equations. The intersection point of the graphs would give the solution.

The slope of the first line is -1

And the slope of the second line is 3

The slopes are not equal. Hence, the line are not parallel.

When we plot the graphs of these equations then the intersection point will give us the solution.

The intersection point is (0.25,3.75).

Hence, the solution is x=0.25, y=3.75

Therefore, first option is correct.

b

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west