Solve algebraically the simultaneous equations x^2 + y^2 = 25, y – 3x = 13
Rearrange y - 3x = 13 to y = 13 + 3xSquare y to give y^2 = 169 +78x +9x^2Sub into first equation to give x^2 + 169 + 78x +9x^2 = 25Simplify to give 10x^2 + 78x + 144 = 0 Apply quadratic formula to solve for x, first x = -3 and second x = -24/5Sub back in to give y values, first y = 4 and second y = -7/5Sub back in to check - Answers are correct.
BH
Related Maths GCSE answers
All answers ▸Solve the equation: 13y − 5 = 9y + 27.
The distance from the Earth to the Sun is 93 million miles. Assume: it takes 365 days for the Earth to travel once around the Sun and the Earth travels in a circle with the Sun at the centre. Work out the average speed of the Earth in miles per hour.
Find the centre and radius of the circle with equation: x^2 + y^2 -4x +8y = 5, and determine whether the point (7,-4) lies on the circle.
Two ordinary fair dice are rolled. Work out the probability that both land on a value less than 4.