Is the following relation a function?
1 answer:
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Answer:
Step-by-step explanation:
arithmetic sequence formula:
where is the first term and
is the common difference
Given:
⇒
⇒
Given:
⇒
⇒
Rearrange the first equation to make the subject:
a = 32 - 9d
Now substitute into the second equation and solve for
(32 - 9d) + 11d = 106
⇒ 32 + 2d = 106
⇒ 2d = 106 - 32 = 74
⇒ d = 74 ÷ 2 = 37
Substitute found value of into the first equation and solve for
:
a + (9 x 37) = 32
a + 333 = 32
a = 32 - 333 = -301
Therefore, the equation is:
Answer:
(a) (5, -3)
Step-by-step explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
<h3>Expression to substitute</h3>The given equations are ...
- y = x -8
- 2x +3y = 1
We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
<h3>Substitution</h3>When the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
<h3>Solution</h3>This 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
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The attached graph confirms this solution.
