Solve these two simultaneous equations.
eq.1 4x+3y=7eq.2 3x+7y=16
You want to eliminate one of the variables (either x or y) reducing the problem to just one equation with one variable which can be solved. This can be done by multiplying each equation by a factor and then subtracting one equation from the other. In this case, eliminating x.
Multiplying eq1. by 3 gives: eq.3 12x+9y=21eq.2 by 4 gives: eq.4 12x+28y=64Then subtracting eq.3 from eq.4 (to give a positive multiple of y, although the opposite calculation could be done) leaves: 19y=43 therefore y=43/19. Subbing this number back into either of the original equations solves for x. A check can be performed by subbing both obtained values into the other equation and ensuring the answer is consistent.
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A bag contains 5 red beads and 7 blue beads. Two beads are removed at random without replacement. Workout the probability that the two beads are the same colour.
Write the number 0.000000001 in standard form.
A)Write x^2 – 8x + 25 in the form (x – a)^ 2 + b. (B) Write down the coordinates of the turning point of the graph of y = x2 – 8x + 25. (C)Hence describe the single transformation which maps the graph of y = x2 onto the graph of y = x2 – 8x + 25.