Let's solve the system of equations to find the intersection point:
We are given the following system of equations:
[tex]\[
\begin{array}{l}
y = -5x + 3 \\
y = 1
\end{array}
\][/tex]
To find the solution, we need to determine the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.
Step 1: Set the two equations equal to each other, since they both equal [tex]\(y\)[/tex]:
[tex]\[
-5x + 3 = 1
\][/tex]
Step 2: Solve for [tex]\(x\)[/tex]:
Subtract 3 from both sides of the equation:
[tex]\[
-5x + 3 - 3 = 1 - 3
\][/tex]
[tex]\[
-5x = -2
\][/tex]
Divide both sides by -5:
[tex]\[
x = \frac{-2}{-5}
\][/tex]
[tex]\[
x = \frac{2}{5}
\][/tex]
So, [tex]\(x = \frac{2}{5}\)[/tex].
Step 3: Substitute [tex]\(x = \frac{2}{5}\)[/tex] back into the second original equation to find [tex]\(y\)[/tex]. However, since the second equation is [tex]\(y = 1\)[/tex], we know that [tex]\(y = 1\)[/tex].
Therefore, the solutions are:
[tex]\[
x = \frac{2}{5} \quad \text{and} \quad y = 1
\][/tex]
Thus, the solution to the system of equations is [tex]\(\left(\frac{2}{5}, 1\right)\)[/tex].
Since [tex]\(\frac{2}{5} = 0.4\)[/tex], the solution in decimal form is [tex]\((0.4, 1)\)[/tex].
So, the correct choice from the given options is:
[tex]\[
(0.4, 1)
\][/tex]
