Question

7x-2y=-13y=4x-11) How many solutions are possible with this type of system of equations and how doyou know?2) How would you solve this system algebraically, what strategy would you use andwhy? Explain how to Solve the system.3) What are 3 different methods for solvina systems of equations and whenwould you use each one?

Answer 1

Given:

$\begin{gathered} 7x-2y=-13 \\ y=4x-1 \end{gathered}$

To Determine: number of possible solutions

Solution

Let us solve for x and y simultaneously using substitution method

$\begin{gathered} Combining\text{ the 2 equations} \\ equation1:7x-2y=-13 \\ equation2:y=4x-1 \end{gathered}$

From equation 2, y = 4x - 1. Let us substitute for y in equation 1

$\begin{gathered} 7x-2(4x-1)=-13 \\ 7x-8x+2=-13 \\ 7x-8x=-13-2 \\ -x=-15 \\ x=15 \end{gathered}$

Substitute x = 15 into equation 2

$\begin{gathered} y=4x-1 \\ y=4(15)-1 \\ y=60-1 \\ y=59 \end{gathered}$

Hence, the solution to the given system of equations is x = 15, y = 59

The system of equations has ONE SOLUTION

The