Question

[4]How many solutions does the system of equations have?y = 7x-4y = 7x + 2 One Soluton Infinite Solutions No Solution

Answer 1

Given system of equations:

`\begin{gathered} y\text{ = 7x - 4} \\ y\text{ = 7x + 2} \end{gathered}`

Let us attempt to solve the equations

From equation 1:

`y\text{ = 7x -4}`

Substituting the expression for y into equation 2:

`\begin{gathered} y\text{ = 7x + 2} \\ 7x\text{ -4 = 7x + 2} \\ \text{Collect like terms} \\ 7x\text{ - 7x = 2 + 4} \\ 0\text{ = 6} \end{gathered}`

This imples that there is no solution to the system of equations.

We can plot the graph of the equations to better visualize and see that the lines don't intersect

The lines are parallel and do not intersect. Hence, there is no solution to the system of equations