To solve the system of equations:
[tex]\[
\begin{array}{l}
y = -5x + 3 \\
y = 1
\end{array}
\][/tex]
we need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously. Here are the steps to solve this system:
1. Substitute the value of [tex]\(y\)[/tex] from the second equation into the first equation:
Given [tex]\( y = 1 \)[/tex] from the second equation, we can substitute this value into the first equation:
[tex]\[
1 = -5x + 3
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Rearrange the equation to isolate [tex]\(x\)[/tex]:
[tex]\[
1 = -5x + 3 \implies -5x = 1 - 3 \implies -5x = -2
\][/tex]
Divide both sides by [tex]\(-5\)[/tex]:
[tex]\[
x = \frac{-2}{-5} = 0.4
\][/tex]
3. Determine the corresponding [tex]\(y\)[/tex] value:
From the second equation [tex]\( y = 1 \)[/tex], we already know that when [tex]\(x = 0.4\)[/tex], [tex]\(y\)[/tex] will be 1.
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (0.4, 1)
\][/tex]
Among the given options, the correct one is:
[tex]\[
(0.4, 1)
\][/tex]
