First Let we solve the Original system of equations:
equation (1): 
equation (2): 
Multiplying equation (1) by 7, we get
Subtracting,
implies 
Then
Thus the solution of the original equation is
Now Let we form the new equation:
Equation 2 is kept unchanged:
Equation (2):
Equation 1 is replaced with the sum of equation 1 and a multiple of equation 2:
Equation (1): 
Now solve this two equations: 
Multiply (1) by 7 and (2) by 8,
Subtracting,
implies
Then x=2.
so the solution for the new system of equation is x=2, y=1.
This Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations
Answer:
20 gallons were used from the tank with the octane rating of 80.
Step-by-step explanation:
Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.
To find : How many gallons should be used from the tank with the octane rating of 80?
Solution : Let x be the volume of gas whose octane rating is 140 and
y be the volume of gas whose octane rating is 80.
Then, we form the equation as:
(1) 
or 
.........[3]
(2) 
Now multiply equation (2) by 4
...........[4]
Subtract (4) from (3)
Put x in equation [4] we get,
Therefore, x=40 and y=20
So, 20 gallons were used from the tank with the octane rating of 80.
The answer is D. "x=-15 or 15."
You can solve this by adding seven on both sides.
|x|-7=8
+7 +7
------------
|x|=15
Therefore, x is either equal to 15 or -15.
It would be A. You can find this out by using SOH CAH TOA,
SOH means sin= opposite/hypotenuse
CAH mean cos= adjacent/hypotenuse
TOA means tangent= opposite/adjacent
You would use CAH since you are trying to find cos∠C
You would have cos∠C=10/26.
26 is the hypotenuse since it is opposite the right angle and is the biggest side.
10 is the adjacent since it is right next to C
You would simplify this down to 5/13 by dividing by 2.
This gives you A.
