Chapter 11.1, Problem 8AYU

To determine

The solution of the given system of equations.

Answer to Problem 8AYU

Solution:

  $(x,y)=(-2,4)$ is the solution.

Explanation of Solution

Given:

  $3x+2y=2$

  $x-7y=-30$

  $x=-2,y=4$

Calculation:

The system of equations is,

  $3x+2y=2$

  $x-7y=-30$

From the second equation we get,

  $x=7y-30$

Substituting this value of $x$ in the first equation we get,

  $3(7y-30)+2y=2$

  $21y-90+2y=2$

  $23y=2+90$

  $23y=92$

  $y=\frac{92}{23}$

  $y=4$

Substituting this value of $y$ in the second equation we get,

  $x-7(4)=-30$

  $x-28=-30$

  $x=-30+28$

  $x=-2$

Thus the solution is $x=-2,y=4$

Therefore the given point (-2,4) satisfies the given system of equations and hence is the solution.