Answer:
(-1, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
10x + 6y = 14
-x - 6y = -23
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Add 2 equations together: 9x = -9
- Divide 9 on both sides: x = -1
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: -x - 6y = -23
- Substitute in <em>x</em>: -(-1) - 6y = -23
- Multiply: 1 - 6y = -23
- Subtract 1 on both sides: -6y = -24
- Divide -6 on both sides: y = 4
Answer:
Here we have the relation:
m = 140*h
Where m is the distance in miles, and h is time in hours.
And we want to complete a table like:
![\left[\begin{array}{ccc}in, h&out, m\\&\\&\\&\\&\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Din%2C%20h%26out%2C%20m%5C%5C%26%5C%5C%26%5C%5C%26%5C%5C%26%5Cend%7Barray%7D%5Cright%5D)
The way to complete this, is to evaluate the function:
m = 140*h
in different values of h, and then record both values of h and m in the table.
Let's use values of h that increase by 0.5, then:
if h = 0.5
m = 140*0.5 = 70
We have the pair: h = 0.5, m = 70
if h = 1
m = 140*1 = 140
We have the pair: h = 1, m = 140
if h = 1.5
m = 140*1.5 = 210
Then we have the pair h = 1.5, m = 210
if h = 2
m = 140*2 = 280
We have the pair: h = 2, m = 280
Now we can complete the table, and it will be:
![\left[\begin{array}{ccc}in, h&out, m\\0.5&70\\1&140\\1.5&210\\2&280\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Din%2C%20h%26out%2C%20m%5C%5C0.5%2670%5C%5C1%26140%5C%5C1.5%26210%5C%5C2%26280%5Cend%7Barray%7D%5Cright%5D)
the diagonal length and probably be 22.2
For line A,
if we increase x by 1 unit then y increases by 4 units i.e. (1,3) and similarly another point becomes
(2,7).
For line B,
if we increase x by 1 uni then y also increases by 1 unit i.e ( 1,1) and similarly another points becomes (2,2),(3,3),(4,4), etc.
For line C,
if we increase x by 3 units then y increases by 1 units i.e.(3,1) and similarly another points becomes
(7,2) and so on.
In above lines, the value of x is exactly equal to that of y in line B.
therefore, line B has constant proportionality between x and y.
The equation would be worded as: 2m+16=36.
Solve! Using the subtraction property of equality, 2m=20. Then the division property of equality lets us figure out that m=10.
