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Solve the simultaneous equations 2x + y = 7 and 3x - y = 8

There are three methods for solving simultaneous equations: elimination, substitution and by using graphs.Elimination is a good method in this case as the y terms are equal in both equations. We just add ...

Answered by Tia J. • Maths tutor

7613 Views

Prove the change of base formula for logarithms. That is, prove that log_a (x) = log_b (x) / log_b (a).

Firstly, recall the definition of a logarithm: if y = log_a(x), then this means that y is the power you have to raise a to, to get x, that is a^y = x.Now, we want to introduce a new ba...

Answered by Tom H. • Maths tutor

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How do you solve the simultaneous equations x^2+y=1 and -x+y=-1

First rearrange the second equation so that it's equal to y. You do this by adding x and y to both sides of the equation. You should then have y=x-1. Next you should sub y=x-1 into the first equation, x

Answered by Chloe M. • Maths tutor

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(ii) Prove by induction that, for all positive integers n, f(n) = 3^(3n–2) + 2^(3n+1) is divisible by 19

Let P(n) represent the statement that 'f(n) is divisible by 19'. For the basis step, I prove that P(1) is true: f(1) = 3^3(1)-2+ 2³⁽¹⁾⁺¹ = 19. 19 is divisible by 19 so P(1) is true. I...

Answered by Daniel L. • Maths tutor

10713 Views

Make x the subject of, 4(x+1)/(x+2) = y

The fundamental rule to keep in the back of your head is 'whatever happens to one side must happen to the other'. This way we can be sure that whatever is on the left hand side of the equals sign will be ...

Answered by Jack W. • Maths tutor

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