algebra?????????????????

Nadina: algebra?????????????????
Write the equation of the line that is parallel to the line given that passes thru the point shown one, four and three eight. there is also a point not on the line at five three
…………………………………………………………………………………………………………………….
solve the following system of equations X +Y=7 2X-3y=-6…………………………………………………………………………..

Answers and Views:

Answer by ireadlots
You have a line passing through (1,4) and (3,8) and you need to find a line parallel to it that passes through (5,3).

Things you need to know:
1) The slope of a line between two points is given by the formula slope = rise/run or
m = (y2-y1)/(x2-x1)
2) If 2 lines are parallel, they have the same slope
3) If a line equation is in the form y = mx+b, m is the slope, and b is the y intercept.

Now, we use this information to solve your problem:

Step 1 – Find the slope of the line
m = (8-4)/(3-1) = 4/2 = 2

Step 3 – Find the equation of a line with slope 2 that passes through (5,3)

y = mx + b
3 = 2*(5) + b
Solve for b
3 = 15 + b
b = 3-15 = -12

So, your line is y = 2x-12

solve the following system of equations
X +Y=7 -> equation 1
2X-3y=-6 -> equation 2
You can do this 2 ways – substitution or elimination – your choice, whichever you think is easier.

1) Substitution
Start by rearranging the first equation to get one value in terms of the other:

x = 7-y

Now plug 7-y into the second equation where is says x

2x – 3y = -6
2(7-y) – 3y = -6
14 – 2y-3y = -6
14-5y = -6
-5y = -20
y = 4

Now x = 7-y = 7-4 = 3

2) Elimination
Start by multiplying every term in the first equation by 2
x+y = 7
2x + 2y = 14
Now subtract the second equation from the first
2x + 2y = 14 –
2x – 3y = -6
—————–
2x – 2x + 2y – (-3y) = 14 – (-6)
2y+3y = 14+6
5y = 20
y = 4
Now solve the first equation for x
x+y = 7
x + 4 = 7
x = 3