Solve the following pair of linear equations by using cross multiplication. ux−vy=wvx−uy=1−w


  1. Home
  2. Math
  3. All Questions
Answer:

x=v(v−u)(v+u)−wv−u and y=u(v−u)(v+u)−wu−v

Step by Step Explanation:
  1. The given system of equations can be written as ux−vy=w  ⟹  ux−vy−w=0vx−uy=1−w  ⟹  vx−uy−(1−w)=0
  2. By cross-multiplication, we have x−v−u↗↘−w−(1−w)=−yuv↗↘−w−(1−w)=1uv↗↘−v−u⟹xv(1−w)−uw=−y−u(1−w)+vw=1−u2+v2⟹xv−vw−uw=−y−u+uw+vw=1−u2+v2⟹xv−w(v+u)=−y−u+w(u+v)=1(v−u)(v+u)⟹x=v−w(v+u)(v−u)(v+u) and y=u−w(u+v)(v−u)(v+u)⟹x=v(v−u)(v+u)−wv−u   and   y=u(v−u)(v+u)−wu−v
  3. Hence, the value of x is v(v−u)(v+u)−wv−u and the value of y is u(v−u)(v+u)−wu−v.

You can reuse this answer
Creative Commons License