Use any method to find the point of intersection of the lines x= 3 and y= -2
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The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
<h3>What is a linear equation?</h3>It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have three linear equations in three variables:
x - y - z = 0 ..(1)
2x - y + 2z = 1 ..(2)
x - y + z = -2 ..(3)
From the equation (1):
Plug this value in the equation (2) and (3):
After solving we get:
z = -1
y = 5
Plug the above two values in equation (1) we get:
x = 4
Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
Learn more about the linear equation here:
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Pictures always help; see the one I've attached for reference.
Call the first vector (from HQ to the supply drop) u and the second vector (from supply drop to medics) v. We then want to find w, the vector from the medics to HQ, which corresponds to the vector -(u + v). (This is because u + v is the vector pointing from HQ to the medics; we're talking about the one in the opposite direction.)
Write the vectors in horizontal/vertical component form:
u = (125 km) (cos 235º x + sin 235º y) = (-71.70 x - 102.39 y) km
v = (75 km) (cos 110º x + sin 110º y) = (-25.65 x + 70.48 y) km
Why these angles?
- "55 degrees south of west" is 235º; due west is 180º from the positive horizontal axis, and you add 55º to this
- "20 degrees west of north" is 110º; due north is 90º, so add 20º to this
Add the vectors:
u + v = (-97.35 x - 31.92 y) km
Multiply by -1 to get the vector w:
w = -(u + v) = (97.35 x + 31.92 y) km
The distance covered by this vector is equal to its magnitude:
||w|| = √((97.35 km)^2 + (31.92 km)^2) = 102.45 km
The direction <em>θ</em> is given by
tan<em>θ</em> = (31.92 km)/(97.35 km) ==> <em>θ</em> = 18.15º
