Answer:
- y=14-2x; 6x+3y=42
- 2x+y=17; -6x=3y-51
Step-by-step explanation:
Dependent equations will have infinite solutions. One way to tell if a system of equations is dependent is to put all of the equations into standard form. Here, we can use the form ...
ax + by = c
where a, b, c are mutually prime integers and "a" is positive. When dependent equations are put in this form, they resolve to the same equation.
Here, the rearrangement is accomplished by putting the x- and y-terms on the same side of the equal sign, with the x-term having a positive coefficient. If necessary, the constant is put on the other side, and any common factors removed from all of them.
Then the sets of equations are ...
- 2x +5y = 31
- 6x -y = 13 . . . . not dependent
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- 2x +y = 10
- 6x +3y = -7 . . . . not dependent
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- 2x +y = 14
- 2x +y = 14 . . . . dependent
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- 2x +y = 13
- 4x -3y = -19 . . . . not dependent
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- 2x +y = 14
- x +2y = 13 . . . . not dependent
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- 2x +y = 17
- 2x +y = 17 . . . . dependent
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The 3rd and 5th sets of equations are dependent, so have infinite solutions.
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The second set of equations is inconsistent, so has no solutions.
Answer:
70 degrees
Step-by-step explanation:
Angles 130 degrees and TUV are supplementary angles. Thus, the latter is (180 - 120), or 60, degrees. Now the sum of all three interior angles of this triangle must be 180 degrees: (60 + 50 + >TUV) = 180, so >TUV is 70 degrees (answer C).
n = 100 (or) 10²
Solution:
Given equation is 1.6 ÷ n = 0.016.
Part A:
To simplify the equation and find the value of n.
1.6 ÷ n = 0.016
Do cross multiplication.
Divide by 0.016 on both sides of the equation.
To remove decimal point multiply and divide by 1000 on left side.
Switch the sides.
n = 100
n = 10²
Hence the value of n is 10².
Part B:
= 0.016
Hence the answer is true.
