Chapter 3.1, Problem 50PPS

To determine

To find:The solution of the system of equations by using elimination,

  $8x+y=27$

  $-3x+4y=3$

Answer to Problem 50PPS

  $x=3,y=3$

Explanation of Solution

Given information:

  $8x+y=27$ …........ (1)

  $-3x+4y=3$ ........ (2)

Calculation:

Multiplying equation (1) by 4 and equation (2) by 1,

  $32x+4y=108$ ………………… (3)

  $-3x+4y=3$ ........ (4)

Subtracting equation (4) from equation (3) to eliminate y,

  $\begin{array}{l}(32x+4y)-(-3x+4y)=108-3\\ \Rightarrow 32x+4y+3x-4y=105\\ \Rightarrow 35x=105\\ \Rightarrow x=\frac{105}{35}\\ \Rightarrow x=3\end{array}$

Substituting the value of x in equation (1),

  $\begin{array}{l}8x+y=27\\ \Rightarrow (8)(3)+y=27\\ \Rightarrow 24+y=27\\ \Rightarrow y=27-24\\ \Rightarrow y=3\end{array}$

Thus, the solution of the system of equations is $x=3,y=3$ .