How do I find these equations using substitution y=-3x+5 and 5x-4y=-3 ?
2 answers:
Answer:
(1,2)
Step-by-step explanation:
1) To solve using substitution, first isolate one of the variables in one of the equations. However, the y in y = -3x + 5 has already been isolated, so we don't need this step. Instead, take that value of y and substitute it for the y in the other equation, 5x - 4y = -3. So, substitute -3x + 5 for the y in 5x - 4y = -3 and solve:
2) So, x = 1. Now, take that value of x and substitute back into any of the equations to find the y value. (I chose to substitute it into y = -3x + 5, but either choice is fine). So, substitute 1 for the x in y = -3x + 5 and solve:
So, y = 2. Thus, by knowing both x and y values, the solution would be (1,2).
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Answer:
E = 64.05
NG = 52.29
O = 35.15
Step-by-step explanation:
With the statement we can create a system of 3X3 equations that would be as follows:
E = electricity
NG = natural gas
O = oil
0.35 * E + 0.15 * NG + 0.25 * O = 25
0.35 * E + 0.15 * NG + 0.2 * O = 15
0.1 * E + 0.1 * NG + 0.1 * O = 20
If we pass this system equations to matrix and subtract it from the identity matrix we would have the following:
0.65 * E - 0.15 * NG - 0.25 * O = 25
-0.35 * E + 0.85 * NG - 0.2 * O = 15
-0.1 * E - 0.1 * NG + 0.9 * O = 20
Solving this system of equations around here can be very long and impractical, therefore, I attach a photo of the process:
And the answer is:
E = 64.05
NG = 52.29
O = 35.15
