Answer:
One solution
Step-by-step explanation:
5x + y = 8
15x + 15y = 14
Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form
So we solve for "y" in the equation "5x + y = 8"
5x + y = 8
Step 1: Subtract 5x from both sides.
5x + y − 5x = 8 − 5x
Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped
y = −5x + 8
Now we can solve using substitution:
We substitute "-5x + 8" into the equation "15x + 15y = 14" for y
So it would look like this:
15x + 15(-5x + 8) = 14
Now we just solve for x
15x + (15)(−5x) + (15)(8) = 14(Distribute)
15x − 75x + 120 = 14
(15x − 75x) + (120) = 14(Combine Like Terms)
−60x + 120 = 14
Step 2: Subtract 120 from both sides.
−60x + 120 − 120 = 14 − 120
−60x = −106
Divide both sides by -60
Simplify
Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"
So there is only one solution to the equation.
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Step-by-step explanation:
the midpoint between 2 points (x1, y1) and (x2, y2) is simply ((x1+x2)/2, (y1+y2)/2).
so,
1.
(9, 7) to (4, -3)
midpoint is ((9+4)/2, (7+ -3)/2) = (13/2, 4/2) = (6.5, 2)
2.
(-7, -5) to (2, 1)
midpoint is ((-7+2)/2, (-5+1)/2) = (-5/2, -4/2) = (-2.5, -2)
3.
now we have the midpoint and need the second point.
(4, 2) over (3, 4) to (x, y)
3 = (4 + x)/2
6 = 4 + x
x = 2
4 = (2 + y)/2
8 = 2 + y
y = 6
4.
(-2, 1) over (-3, 2) to (x, y)
-3 = (-2 + x)/2
-6 = -2 + x
x = -4
2 = (1 + y)/2
4 = 1 + y
y = 3