Solve algebraically the simultaneous equations x^2 + y^2 = 25 and y - 3x = 13
Start to solve by substitution: eqn 1 x^2 + y^2 = 25eqn 2 y - 3x = 13 => y = 3x + 13Substitute eqn 2 into 1: x^2 + (3x +13)^2 = 25expand and simplify the equation ...5x^2 + 39x + 72 = 0Factorise the equation: (5x+24)(x+3) = 05x = -24 => x = -24/5x = -3Substitute back into equation 2 to find equivalent y values: x = -3 and y = 4, x = -24/5 and y = -7/5
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