Chapter 9.6, Problem 1MRE

To determine

Tofind:the solution of each system using addition and subtraction method.

Answer to Problem 1MRE

The coordinate of given two equation is $\left(5,-2\right)$ .

Explanation of Solution

Given:

  $\text{3x+2y=11}$ .

  $\text{x-y=7}$ .

Concept used:

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

According to the given equation:

  $\text{3x+2y=11}$ ………. $\left(\text{i}\right)$

  $\text{x-y=7}$ …………… $\left(\text{ii}\right)$

Multiplying the second equation by $\text{2}$ :

  $\text{2x-2y=14}$ ……… $\left(\text{iii}\right)$

Solving equation $\left(\text{i}\right)$ and $\left(\text{iii}\right)$ by adding the two equation:

  $\text{5x=25}$ .

Diving both side by $\text{5}$ :

  $\text{x=5}$ .

By substituting the $\text{x=5}$ in $\text{x-y=7}$ to find the value of $\text{y}$ :

  $\text{5-y=7}$ .

  $\text{y=-2}$ .

Hence, the coordinate of given two equation is $\left(5,-2\right)$ .