Chapter 3, Problem 10CR

To determine

To calculate : The solution of the given system of equations.

Answer to Problem 10CR

  $x=-2,y=5$

The correct option is C $(-2,5)$

Explanation of Solution

Given information : Given equations are:

  $4x+3y=7$

  $-2x+y=9$

Formula used : Elimination method

The method in which we eliminate one of the variable by adding or subtracting the equation to get the solution.

Calculation:

Considering the equations

  $4x+3y=7$

  $-2x+y=9$

Multiply the equation $-2x+y=9$ by $2$ and add it into equation $4x+3y=7$ , we get

  $5y=25$

  $y=5$

Put the value $y=5$ in equation $4x+3y=7$ , we get

  $4x=-8$

  $x=-2$

  $4x+3y=7$ Now, we can check out the solution by plugging the values in given equations

  $4(-2)+3(5)=7$

  $-8+15=7$

  $7=7$

  $-2x+y=9$

  $-2(-2)+5=9$

  $4+5=9$$\begin{array}{l}9=9\\ \end{array}$

In both the cases we get the true statement.