Solve the simultaneous equations y = x^2 +3x and y = x+8
Because both of the equations are equal to y, the first thing we do is make them equal to each other:x^2 + 3x= x + 8We then want to rearrange the equation so that everything is on the same side of the equals sign, so that the equation is equal to 0:x^2 + 3x - x - 8 = 0We can then simplify this down to be:x^2 + 2x - 8 = 0The simplest method to find x from the above equation is to factorise. This is where we create two sets of brackets from the equation. To put the equation into brackets, we need to find two numbers that multiply together to make -8 and add together to make 2. These numbers are +4 and -2, which are put into the brackets as follows:(x+4)(x-2) = 0If the product of two brackets is 0, then one or both brackets must also be equal to 0. To solve, put each bracket equal to 0:x+4 = 0x = -4x-2 = 0x = 2To find the value for y, substitute these values of x back into the original equation.y = x + 8 when x = -4y = -4 + 8 y = 4y = x + 8 when x = 2y = 2 + 8y = 10The answers are now in pairs: when x = -4, y = 4 and when x = 2, y = 10
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