Answer:
B
Step-by-step explanation:
First label the equations.
6x +3y= 18 -----(1)
y= -2x +5 -----(2)
subst. (2) into (1):
6x +3(-2x +5)= 18
6x +3(-2x) +3(5)= 18 (expand)
6x -6x +15= 18
15= 18 (simplify)
(reject)
There is no solution.
<u>Further explanation</u><u>:</u>
If I rewrite the first equation into the form of y=mx+c, I would get
6x +3y=18
3y= 18 -6x (bring y term to one side)
y= 6- 2x (÷3 throughout)
y= -2x +6
Notice that the gradients of both lines are equal ( -2). This implies that they are parallel to each other and will never meet. Hence there are no solutions.
In this diagram we see that 80 and 3x+4y are both vertical angles and vertical angles are congruent or always equal so we can set those two equations equal to each other then we can see that a line splits two angles making them supplementary (they equal 180 degrees) So we can have another equation, the two equations are:
3x+4y=80 and 3x+4y+7x-8y=180 (add like terms to simplify and get 10x-4y=180
Then use elimination to get rid of the y variables
10x-4y=180 (plus)
+3x+4y=80 (the negative 4 and positive 4 cancels each other out so you are left with:)
13x=160 (divide by x)
x=12.30769 which can be rounded to x=12.31
Then we have to plug in x into the first equation:
3(12.31) + 4y = 80
36.93 + 4y = 80 (subtract 36.93 from 80)
4y = 43.07 (divide)
y=10.7675 or rounded to 10.77
so x=12.31 and y=10.77
Answer:
D. {(1,2) , (2,3) , (3,4) , (4,5)}
Step-by-step explanation:
Functions are relations with one output for any unique input. Relations that pass the vertical line test have one output for each input. In this case, D was the only set that met the criteria.
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