Given the system of equations 2 x − 3 y − 9 z = 9 x + 3 z = 3 − 3 x + y − 4 z = − 10 (a) determine whether the system is inconsistent or dependent; your answer is (input inconsistent or dependent) dependent correct (b) if your answer is dependent in (a), find the complete solution. write x and y as functions of z .

Dependent

Step-by-step explanation:

We are given that system of equations

(Equation I)

( Equation II)

(Equation III)

Equation III multiply by 3 and then add to equation I then we get

Divided by -7 then we get

Now , obtained equation subtract from equation II then we get

0=0

Hence, equation II is a linear combination of equation I and equation III.

Therefore, system is dependent because system has infinite solutions.

Substitute the value of x in equation I then we get

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.