Question

Use cramers rule to solve 4x+3y=4 -3x-y=7 show your work

Answer 1

$\left\{\begin{array}{ccc}4x+3y=4\\-3x-y=7\end{array}\right\\\\D= \left|\begin{array}{ccc}4&3\\-3&-1\end{array}\right|=(4)(-1)-(-3)(3)=-4+9=5\\\\D_x=\left|\begin{array}{ccc}4&3\\7&-1\end{array}\right|=(4)(-1)-(7)(3)=-4-21=-25\\\\D_y=\left|\begin{array}{ccc}4&4\\-3&7\end{array}\right|=(4)(7)-(-3)(4)=28+12=40\\\\x=\dfrac{D_x}{D}\Rightarrow x=\dfrac{-25}{5}=-5\\\\y=\dfrac{D_y}{D}\Rightarrow y=\dfrac{40}{5}=8$