What is the solution to the system of equations?
-3x + y = -1
2x + y = 14

a (3, 8)
b (-8, 3)
c (-3, 8)
d (8, 3)

The answer is A.

Step-by-step explanation:

I used the elimination method to solve this system of equations.

The elimination method is where you add both of the equations, where one of the variables are equal in terms of number, but the signs are flipped. That's because you add the equations, crossing out one of the variables, leaving you with one variable to easily solve with.

It goes like this:

I multiplied the first equation (-3x+y=-1) by -1, to be able to cross out the y variable when I add.

So, after multiplying, the equation would be: 3x-y=1

Now, you add the two equations together.

  3x-y=1

  2x+y=14

+

  5x=15

Solving we get x=3.

That already gives you a as an answer, but let's continue.

Now we plug x=3 back into one of the equations to find what y is.

2(3)+y=14

6+y=14

y=8

So, the answer is A, (3, 8).

Checking: Just plug the numbers back in to see if they're right.

-3(3)+8= -1

-9+8=-1

-1=-1  

Hope this helps!

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph