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CanadaON
Grade 11

EXT: Systems of straight lines and circles

Interactive practice questions

Consider the following system of equations:

$x^2+y^2$x2+y2 $=$= $4$4
$3x+4y$3x+4y $=$= $0$0

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a

By filling in the missing values, verify that the points of intersection on the graphs are solutions of the corresponding system of equations.

First, test the point $\left(\frac{8}{5},-\frac{6}{5}\right)$(85,65).

$x^2+y^2=4$x2+y2=4

           
$LHS$LHS $=$= $\left(\editable{}\right)^2+\left(\editable{}\right)^2$()2+()2   $RHS$RHS $=$= $\editable{}$
  $=$= $\frac{64}{25}+\editable{}$6425+        
  $=$= $\frac{\editable{}}{25}$25        
  $=$= $\editable{}$        
             

$3x+4y=0$3x+4y=0

           
$LHS$LHS $=$= $3\times\editable{}+4\times\editable{}$3×+4×   $RHS$RHS $=$= $\editable{}$
  $=$= $\editable{}+\left(-\frac{24}{5}\right)$+(245)        
  $=$= $\editable{}$        
b

Now test the point $\left(-\frac{8}{5},\frac{6}{5}\right)$(85,65).

$x^2+y^2=4$x2+y2=4

           
$LHS$LHS $=$= $\left(\frac{\editable{}}{\editable{}}\right)^2+\left(\frac{\editable{}}{\editable{}}\right)^2$()2+()2   $RHS$RHS $=$= $\editable{}$
  $=$= $\editable{}+\frac{36}{25}$+3625        
  $=$= $\frac{\editable{}}{25}$25        
  $=$= $\editable{}$        
             

$3x+4y=0$3x+4y=0

           
$LHS$LHS $=$= $3\times\editable{}+4\times\editable{}$3×+4×   $RHS$RHS $=$= $\editable{}$
  $=$= $-\frac{24}{5}+\editable{}$245+        
  $=$= $\editable{}$        
Easy
6min

Consider the system of equations.

$x^2+y^2=10$x2+y2=10

$x-y=2$xy=2

Easy
4min

Consider the system of equations.

$x^2+y^2=2$x2+y2=2

$-3x+2y=5$3x+2y=5

Easy
10min

A system of two equations in two variables whose graphs are a parabola and a circle can have four real ordered-pair solutions.

Easy
< 1min
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