Question

Solve the system. Enter the smallest x-coordinate first

Answer 1

$y= 3 \,\,,\,\,x= -2 \,\,and\,\, y=3\,\,,\,\, x=2$

Step-by-step explanation:

Solving the following system of equations:

$x^2-y=1\\2x^2+y^2=17$

Let

$x^2-y=1\,\,\,(1)\\2x^2+y^2=17\,\,\,(2)$

Putting value of x^2 in eq(2)

$x^2 = 1+y\\Putting\,\,value\,\,of\,\,x^2\,\,in\,\,eq(2)\\2(1+y)+y^2=17\\2+2y+y^2=17\\y^2+2y+2-17=0\\y^2+2y-15=0\\Factorizing:\\y^2-3y+5y-15=0\\y(y-3)+5(y-3)=0\\(y+5)(y-3)=0\\y+5=0 \,\,and \,\, y-3=0\\y = -5 \,\,and \,\, y=3$

Now, finding value of x

Putting y=-5

$x^2 = 1+y\\x^2=1-5\\x^2=-4\\Taking\,\,square\,\,root\\x= \pm2i$

y=-5, x= 2i and y=-5 , x= -2i

Since we need to find x and y coordinates and its value cannot be in terms of i so we will not consider these as answer

Putting y=3

$x^2 = 1+y\\x^2=1+3\\x^2=4\\Taking\,\,square\,\,root\\x= \pm2$

So, $y= 3 \,\,,\,\,x= -2 \,\,and\,\, y=3\,\,,\,\, x=2$

Keywords: system of equations

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