SOLUTION: solve the simultaneous Equations 3a^2 - 4y = -1, 2a - y = 1

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Question 1209190: solve the simultaneous Equations 3a^2 - 4y = -1, 2a - y = 1
Found 2 solutions by ikleyn, timofer:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve the simultaneous Equations 3a^2 - 4y = -1, 2a - y = 1
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From the second equation, express  y = 2a-1  and substitute it into first equation.
You will get

    3a^2 - 4(2a-1) = -1,

    3a^2 - 8a + 4 = -1,

    3a^2 - 8a + 5 = 0,


apply the quadratic formula

    a%5B1%2C2%5D = %288+%2B-+sqrt%28%28-8%29%5E2+-+4%2A3%2A5%29%29%2F%282%2A3%29 = %288+%2B-+2%29%2F6.


So, there are two options for "a": they are

    a = 10%2F6 = 5%2F3  and  a = 1.


Now find y for each value of "a", using y = 2a-1.

From this point, can you complete on your own ?



Answer by timofer(104) About Me  (Show Source):
You can put this solution on YOUR website!
system%283a%5E2-4y=-1%2C+y=2a-1%29

3a%5E2-4%282a-1%29=-1, substitution for y
3a%5E2-8a%2B4=-1
3a%5E2-8a%2B5=0
discriminant, just in case, %28-8%29%5E2-4%2A3%2A5=64-60=4=2%5E2
a=%288%2B-+sqrt%282%5E2%29%29%2F6
a=%288%2B-+2%29%2F6
system%28a=1%2Cor%2C5%2F3%29

If a=1 then y=1.
If a=5/3 then y=2%285%2F3%29-1=10%2F3-3%2F3=7%2F3;
so (1,1) or ( 5/3, 7/3 ).

Check for any possible mistakes.