Chapter 3.1, Problem 4CYU

To determine

To Graph: the given system of equations $y=-x-9$ and $3y=5x+5$ and check consistency.

Answer to Problem 4CYU

Consistent equation $\left(-4,-5\right)$

Explanation of Solution

Given:

System of equations are given as.

  $\begin{array}{l}y=-x-9\text{eq}\text{.}\left(1\right)\\ 3y=5x+5\text{eq}\text{.}\left(2\right)\end{array}$

Calculation:

now, solving the given equation 1 &2 we get

  $\begin{array}{l}y=-x-9\text{eq}\text{.}\left(1\right)\\ x+y=-9\text{eq}\text{.}\left(3\right)\end{array}$

  $\begin{array}{l}3y=5x+5\text{eq}\text{.}\left(2\right)\\ -5x+3y=5\text{eq}\text{.}\left(4\right)\end{array}$

Both equation 2 & 4 are linear equations therefore it will straight line on graph.

Draw $x+y=-9$ equation as one of the coordinates $\left(0,-9\right)\&\left(-9,0\right)$ satisfying the equation.

Draw $-5x+3y=5$ equation as one of the coordinates $\left(0,\frac{5}{3}\right)\&\left(-1,0\right)$ satisfying the equation.

Graph is drawn below.

  

Since, lines are intersecting to each other and there is a point of intersection therefore system of equations are consistent and has a solution.

Now, solving equation 3 & 4 we get

  $\begin{array}{l}x+y=-9\\ -5x+3y=5\\ \text{multiplying eq}\text{.}\left(3\right)\text{ by 5 \& eq}\text{.}\left(4\right)\text{ by 1 then we get,}\\ \underset{\_}{\begin{array}{l}5x+5y=-45\\ -5x+3y=5\end{array}}\\ 0+8y=-40\\ 8y=-40\\ y=\frac{-40}{8}\\ y=-5\\ \text{now substitute the value of y in eq}\text{.}\left(3\right)\\ x+y=-9\\ x-5=-9\\ x=-9+5\\ x=-4\\ \end{array}$