Chapter 7.1, Problem 8E

To determine

ToSolveThe system of equations $x-4y=-11$ and $x+3y=3$ by method of substitution and check solution(s) graphically.

Answer to Problem 8E

The solution is of the given system of equation is $\left(x,y\right)=\left(-3,2\right)$

Explanation of Solution

Given:

The system of equations $x-4y=-11$ and $x+3y=3$

Concept Used:

For solving the system of equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$ with substituting method.

The first step is the take out the value of $x$ from first equation i.e., $x=\frac{c_1-b_{1}y}{a}$ and then substitute this value in the second equation to find the value of $y$ . And then use that value of $y$ to find the value of $x$ using $x=\frac{c_1-b_{1}y}{a}$ .

Calculation:

For the given system of equations $x-4y=-11$ and

Let $x-4y=-11------\left(1\right)$

  $x+3y=3------\left(2\right)$

From equation 1, we have

  $x-4y=-11$

i.e., $x=-11+4y------\left(3\right)$

Substituting in equation 2, we have

i.e., $x+3y=3$

i.e., $\begin{array}{c}-11+4y+3y=3\\ -11+7y=3\\ 7y=3+11\\ 7y=14\\ y=\frac{14}{7}\\ y=2\end{array}$

Substituting in equation 3, we have

i.e., $\begin{array}{c}x=-11+4\left(2\right)\\ x=-11+8\\ x=-3\end{array}$

Therefore, the solution of the given system of equation is $\left(x,y\right)=\left(-3,2\right)$

From the given graph of system of equation

  

The solution is of the given system of equation is $\left(x,y\right)=\left(-3,2\right)$

Conclusion:

The solution is of the given system of equation is $\left(x,y\right)=\left(-3,2\right)$ .