Non-Linear Simultaneous Equations (H)

 $x^2+y^2=19$  
 $y=x+5$  
What is the correct next step to solve these simultaneous equations?

•  $x^2+x^2+25=19$  

•  $x^2+y^2=19$  
   $y^2=x^2+25$  
  

•  $x^2+\left(x+5\right)^2=19$  

•  $x+y=\sqrt{19}$  
   $y=x+5$  
  

 $x^2+\left(x+5\right)^2=19$  
What is the correct next step to solve these simultaneous equations?

•  $x^2+x^2+10x+25=19$  

•  $x^2+x^2+10x+10=19$  

•  $x^2+x^2+10=19$  

•  $x^2+x^2+25=19$  

 $x^2+x^2+10x+25=19$  
What's the next step?

•  $2x^2+10x=-6$  

•  $x+x+10=0$  

•  $2x^2+10x+6=0$  

•  $2x^2+10x-6=0$  

 $2x^2+10x+6=0$  
What's the next step?

•  $x=\frac{-2\pm\sqrt{10^2-4\times12}}{20}$  

•  $x=\frac{-10\pm\sqrt{10^2-4\times12}}{4}$  

•  $x=\frac{10\pm\sqrt{10^2-4\times12}}{4}$  

•  $x=-10\pm\frac{\sqrt{10^2-4\times12}}{4}$  

 $x=\frac{-10\pm\sqrt{10^2-4\times12}}{4}$  
Using your calculator, what are the two solutions?

•  $x=-5.541$  
   $x=0.541$  
  

•  $x=-8.197$  
   $x=-11.803$  
  

•  $x=-0.697$  
   $x=-4.303$  
  

•  $x=-6.394$  
   $x=-13.606$  
  

 $x^2+y^2=19$  
 $y=x+5$  
Solve for y.

•  $y=4.303$  
   $y=0.697$  
  

•  $y=-5.697$  
   $y=-9.303$  
  

•  $y=5.697$  
   $y=9.303$  
  

•  $y=-4.303$  
   $y=-0.697$  
  

 $x^2+y^2=19$  

 $y=x+5$  

Which diagram represents these two equations?

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• 
• 
• 

 $x^2+y^2=16$  and  $x+y=4$  have been drawn on the axes. What are the solutions?

•  $\left(4,0\right)$  

•  $\left(-4,0\right)and\left(0,-4\right)$  

•  $\left(4,4\right)$  

•  $\left(4,0\right)and\left(0,4\right)$  

 $y=x^2$  

 $y=x+2$  

What are the correct solution(s) for the pair of simultaneous equations:

•  $x=-1,\ y=1$  and
   $x=2,\ y=4$  
  

•  $x=-1,\ y=1$  

•  $x=-1\ and\ 2$  

•  $x=1,\ y=1$  and
   $x=2,\ y=4$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

 $y=x^2$  and  $y=6x-8$  

Solve this pair of equations.

•  $x=-4,\ y=-16$  and  $x=2,\ y=4$  

•  $x=16,\ y=2$  and  $x=14,\ y=4$  

•  $x=4,\ y=16$  and  $x=2,\ y=4$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11