The equation 3x - 2y = 8 and 6x - 4y = 16 are systems of equations with infinite solutions.
A linear system of equations can have (a)unique solutions, (b) infinite number of solutions, or (c) no solution.
For it to have infinite number of solutions, the graph of the equations must intercept with each other at infinite points, leaving the two graphs overlaying each other.
Given the equation, 3x - 2y = 8, the other equation in a linear system to have infinite number of solutions with it must be the exact same line.
To do this, simply multiply the whole equation with a real number.
Example:
Multiplying the whole equation by 2 gives 6x - 4y = 16.
Now, 3x - 2y = 8 and 6x - 4y = 16 are equations in a linear system with infinite number of solutions.
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Answer:
10 pounds.
Step-by-step explanation:
Let x pounds be the amount of mixed nuts we require.
Amount of peanuts in this mix = 0.70x pounds. Amount of peanuts in the 20% mix = 0.20*15 = 3 pounds.
So we have the equation:-
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10.
The answer is B: <span> a^12/b^6
Proof:
Simplify the following:
(a^4/b^2)^3
Multiply each exponent in a^4/b^2 by 3:
(a^(3×4))/((b^2)^3)
3×4 = 12:
a^12/(b^2)^3
Multiply exponents. (b^2)^3 = b^(2×3):
a^12/b^(2×3)
2×3 = 6:
Answer: a^12/b^6</span>
An easy way to do this is to do trial and error.
All possible places to put the bracket:
a) (25 - 8) - 2 = 19 But since BEDMAS goes from left to right with Addition and Subtraction, the equation is unaffected.
b) 25 - (8 - 2) = 19
25 - 6 = 19
Therefore b) is correct.
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