How do you solve the simultaneous equations #y = x^2- 2# and # y = 3x + 8#?
2 Answers
x = 5 , y= 23 and x = -2 , y = 2.
Explanation:
Here, we have a quadratic and a linear equation which can be solved by the substitution method.
From the second equation, know
put this in place of
Rearrange
It can be factorized :
Therefore,
Plugging it into the second equation we get
So we get the solution as
Explanation:
#"Since both equations give y in terms of x we can equate"#
#"them"#
#rArrx^2-2=3x+8#
#"rearrange into standard form"# y
#rArrx^2-3x-10=0larrcolor(blue)"in standard form"#
#"the factors of - 10 which sum to - 3 are - 5 and + 2"#
#rArr(x-5)(x+2)=0#
#"equate each factor to zero and solve for x"#
#x-5=0rArrx=5#
#x+2=0rArrx=-2#
#"substitute these values into "y=3x+x#
#x=5rArry=(3xx5)+8=23#
#x=-2rArry=(3xx-2)+8=2#
#"the solutions are "(5,23)" and "(-2,2)#
graph{(y-3x-8)(y-x^2+2)((x+2)^2+(y-2)^2-0.04)((x-5)^2+(y-23)^2-0.04)=0 [-10, 10, -5, 5]}