Systems of Equations (Elimination) Test Prep AK

edboost

1. B

$$\eqalign{y=&2x+2\\3x+2y=&4\\\text{Rearrange}\\-2x+y=&2\\3x+2y=&4\\\text{Multiply top equation by -2}\\4x\cancel{-2y}=&-4\\3x\cancel{+2y}=&4\\\hline 7x=&0\\x=&0\\\text{Plug in x to solve for y}\\y=&2(0)+2\\y=&2}$$

 

2. C

 

$$\eqalign{4a+2b&=14\\a+3b&=6\\\text{Multiply bottom equation by -4}\\\cancel{4a}+2b&=14\\\cancel{-4a}-12b&=-24\\\hline-10b&=-10\\b&=1\\\text{Plug in b to find a}\\a+3(1)&=6\\a+3&=6\\a&=3\\(a,b)=(3,1)\\ab=3}$$

3. D

$$\eqalign{\text{The first equation is:}\\y&=3x+b\\\text{Plug in (x,y)}\\1&=3(0)+b\\1&=b\\y&=3x+1}$$

$$\eqalign{\text{The second equation is:}\\m=\dfrac{6-4}{5-3}=\dfrac{2}{2}=1\\y&=1x+b\\\text{Plug in (x,y)}\\4&=1(3)+b\\1&=b\\y&=x+1}$$

$$\eqalign{y&=3x+1\\y&=x+1\\\text{Multiply bottom equation by -3}\\y&=\cancel{3x}+1\\-3y&=\cancel{-3x}-3\\\hline -2y&=-2\\y=1\\\text{Plug in y to find x}\\1&=3x+1\\0&=3x\\0=x}$$

4. A

Before you do the work to figure out this system of equations, note that they both pass through the origin (0,0).  Unless they are the same line (and that answer is not available below) that must be the solution. (x,y)=(0,0), so xy=0.