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How do i solve the simultaneous equations 7x+y=1 and 2x^2-y=3?

First, label the equations 1 and 2:1: 7x+y=1 and 2: 2x^2-y=3Rearrange equation 2 in terms of yy=2x^2-3Now substitue the rearranged version of equation 2 into 1 to give7x+2x^2-3=1.Bring all the values to the ...
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Answered by Irida N. • Maths tutor
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Factorise 2(x^2) +7x+3

Only factors of 2 are 1 and 2, therefore solution will take form of (2x + a)(x + b) to get 2x 2 term. Only factors of 3 are 1 and 3 therefore a and b are either 1 or 3. Playing around and intuition leads us ...
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Answered by Albert R. • Maths tutor
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Simplify (3x^2 + x -2)/(x^2 - 1)

First notice that no simplifications can be made to the problem without changing the form. We start by factorising the numerator. The highest power of x in this question is 2, therefore we know that it has t...
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Answered by Arjun A. • Maths tutor
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Determine the equation of the line which is perpendicular to y = 2x + 9 and crosses through the point (1,2)

When multiplied together the gradients of perpendicular lines should give the answer - 1So: x 1 x 2 = -1x 1 = 2 x 2 = -1/2It crosses through the point (1,2)y = ax+ ba = -1/2y = 22 = -1/2 + bb = 5/2so the equ...
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Answered by Aneisha D. • Maths tutor
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A linear sequence starts: a+2b, a+6b, a+10b, ..., ... The 2nd term has a value of 8. The 5th term has a value of 44. Work out the values of a and b.

We know the values for the 2nd and 5th terms and already have the 2nd term as an equation but not the 5th. Therefore, we need to start by working out what exactly the 5th term is in terms of a and b. From lo...
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Answered by Molly T. • Maths tutor
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