Chapter 6.3, Problem 5STP

For Exercises $1-5,$ choose the correct letter.

What is the solution of the following system of equations?

$5x+7y=3$

$2x=-3y+1$

A. $(11,17)$

B. $(2,-1)$

C. $(11.5,8)$

D. $(-2,1)$

To determine

What is the solution of system of equations $5x+7y=3\text{ and }2x=-3y+1$ .

Answer to Problem 5STP

The solution for the given equations is $x=2\text{and }y=-1$ , so option (B) is correct.

Explanation of Solution

Given information: The given equations are,

  $\begin{array}{c}5x+7y=3\mathrm{....}\left(1\right)\\ 2x=-3y+1\mathrm{....}\left(2\right)\end{array}$

Calculation: From (2) $x=\frac{-3y+1}{2}$ substitute in (1) and simplify,

  $\begin{array}{c}5\left(\frac{-3y+1}{2}\right)+7y=3\mathrm{....}\left(\text{For }x=\frac{-3y+1}{2}\right)\\ -15y+5+14y=6\\ -y=1\\ y=-1\end{array}$

Substitute $y=-1$ in (2),

  $\begin{array}{c}5x+7\left(-1\right)=3\mathrm{....}\left(\text{For }y=-1\right)\\ 5x=10\\ x=2\end{array}$

Hence the solution for the given equations is $x=2\text{and }y=-1$ , so option (B) is correct.