Answer:
Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down
to one with only one variable (by substitution or addition). With three variables
we will reduce the system down to one with two variables (usually by addition),
which we can then solve by either addition or substitution.
To reduce from three variables down to two it is very important to keep the work
organized. We will use addition with two equations to eliminate one variable.
This new equation we will call (A). Then we will use a different pair of equations
and use addition to eliminate the same variable. This second new equation we
will call (B). Once we have done this we will have two equations (A) and (B)
with the same two variables that we can solve using either method. This is shown
in the following examples.
Example 1.
3x +2y − z = − 1
− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations
5x +2y − z = 3
Step-by-step explanation:
Step-by-step explanation:
The above sequence is a geometric sequence
For an nth term in a geometric sequence

where
n is the number of terms
a is the first term
r is the common ratio
From the question
a = 5
r = 10/5 = 2
Therefore the explicit formula for this sequence is

Hope this helps you
When you see questions of this nature, test the individual inequalities and look out for their intersection.
For

Choose a point in the lower or upper half plane created by the line

The above line is the one which goes through the origin.
Now testing (1,0) yields,

That is,

This statement is true. So we shade the lower half of

For

We test for the origin because, it is not passing through the origin.

This yields

This statement is false so we shade the upper half.
The intersection is the region shaded in B. The top right graph
Answer:
z = 1
Step-by-step explanation:
90/15 = 6/z
Cross Multiply
15 * 6 = 90 * z
90 = 90z
Divide both sides of the equation by 90
z = 1
Hope this was useful to you!
Answer:
<em>y - 7 = 1 (x-5)</em>
Step-by-step explanation:
The point slope equation of a line is expressed as;
y - y0 = m(x-x0)
m is the slope
(x0, y0) is the point on the line
Given the following
m = 1
(x0, y0) = (5, 7)
Substitute into the formula
y - 7 = 1 (x - 5)
y - 7 = x -5
y = x - 5 + 7
y = x + 2
<em>Hence the point slope equation of the line is y - 7 = 1 (x-5)</em>
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