Find the value of X and Y if X^2 + Y^2 = 13 and 2X + Y = 1
Firstly, since only one equation is linear, substitution must be used. This will allow us to make a quadratic equation with one variable and solve for X and Y. To do this, I will make Y the subject of the formula, thus 2X + Y = 1 becomes Y = 1 - 2X. Now, we can substitute this in for Y into the quadratic equation containing two variables, allowing us to form a quadratic equation with a single variable. Therefore, X2 + Y2 = 13 becomes X2 + (1 - 2X)2 = 13. Now, we can expand the bracket and simplify, forming the quadratic equation: 5X2 - 4X + 1 = 13. If we equate this equation to 0 and factorise to form (5X + 6)(X - 2) = 0, we can solve to find two solutions for X. Therefore, X must be -6/5 or X must be 2. We can substitute these values of X back into our equation 2X + Y = 1 and solve to find Y. Therefore, Y must be 17/5 or Y must be -3.
