Indices, Log and Simultaneous Equations

Solve the simultaenous equations

 $3x^2-xy+2y^2=16$ 
 $2y-x=4$  

•  $x=-2,\ y=1$ 
  
    $x=\frac{4}{3},\ y=\frac{8}{3}$  

•  $x=\frac{4}{3},\ y=\frac{8}{3}$ 
  
  
  

•  $x=\frac{4}{3},\ y=1$  

•  $x=\frac{8}{3},\ y=\frac{4}{3}$ 
  
   $x=1,\ y=-2$  
  

Solve the simultaneous equations
 $2^{5x}\times4^y=\frac{1}{8}$ 

 $7^x\times49^{2y}=1$  

•  $x=-\frac{2}{3},\ y=\frac{1}{6}$  

•  $x=\frac{1}{6},\ y=-\frac{2}{3}$  

•  $x=-2,\ y=1$  

•  $x=-3,\ y=6$  

Solve the following simultaneous equations, giving your answer in the for

 $a+b\sqrt{3}$  where  $a$  and $b$  are integers.

 $2x+y=9$ 

 $\sqrt{3}x+2y=5$  

•  $x=4+\sqrt{3},\ \ y=1-2\sqrt{3}$  

•  $x=\sqrt{3},\ \ y=-2\sqrt{3}$  

•  $x=1-2\sqrt{3},\ \ y=4+\sqrt{3}$  

•  $x=4-\sqrt{3},\ \ y=1+2\sqrt{3}$  

Solve the simultaneous equations

 $\log_2\left(x+4\right)=2\log_2y$ 
 $\log_2\left(7y-x\right)=4$  

•  $x=5\ or\ 12,\ \ y=3\ \ or\ 4$  

•  $x=3\ or\ 4,\ \ y=5\ \ or\ 12$  

•  $x=5\ or\ -12,\ \ y=-3\ \ or\ 4$  

•  $x=-5\ or\ 12,\ \ y=3\ \ or\ -4$  

Solve the simultaneous equations

 $\frac{8^{\left(p+1\right)}}{4^q}=2^{11}$ 
 $\frac{3^{\left(2p+5\right)}}{27^{\left(\frac{1}{3}\right)}}=9^{3q}$  

•  $p=2,\ q=4$  

•  $p=4,\ q=2$  

•  $p=-4,\ q=-2$  

•  $p=-2,\ q=-4$