Solve the simultaneous equations x^2 +8y=20 and y=x+4

To begin you must substitute the value of y provided into the first equation. The would change the equation into the following form:x^2+8(x+4)=20. Now expand the bracket so that the equation becomes:x^2+8x+32=20.Now subtract 20 from both sides to form a quadratic equationx^2+8x+12=0.Factorise the equation into (x+6)(x+2)=0 As 6 and 2 multiply to make 12 and add together to make 8. You can find all the factor pairs of twelve and check them to see if the add to make 8 in an exam to make sure there are no other possible answers. Since one of the two brackets must be equal to 0 x must be either -6 or -2 for this question. Substitute one of the values of x into the second equation provided.y=-6+4=-2. Therefore when x=-6, y=-2Repeat with the other value of x.y=-2+4=2. Therefore when x=-2, y-=2. In an exam remember to show your working as even if you come to the wrong answer you may still score some method marks which may boost your overall grade.

Answered by Anthony M. Maths tutor

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