Question

1. Identify the solution to the system shown. Show the solution on the graph and
on the table.

Answer 1

The solution to the system of equations
`\(Y_1 = -x + 8\)` and
`\(Y_2 = 5x - 4\)` is x = 3 and y = 5. The values satisfy both equations simultaneously, representing the intersection point on the graph.

To find the solution to the system of equations Y_1 = -x + 8 and Y_2 = 5x - 4, set the two expressions equal to each other since they represent y:

`\[\begin{align*}-Y_1 & = Y_2 \\-x + 8 & = 5x - 4\end{align*}\]`
`- Y_(1) = Y_(2)\\- x + 8 = 5x - 4`

Now, solve for x:

`\[\begin{align*}4x & = 12 \\x & = 3\end{align*}\]`4x = 12

x = 3

Now that you have the value of x, substitute it back into either equation to find the corresponding y. Let's use
`\(Y_1\)`:

`\[\begin{align*}Y_1 & = -x + 8 \\Y_1 & = -3 + 8 \\Y_1 & = 5\end{align*}\]`
`Y_(1) = - x + 8\\Y_(1) = - 3 + 8\\Y_(1) = 5`

So, the solution to the system is x = 3 and y = 5.