To solve the system of equations:
[tex]\[
\begin{array}{l}
y = -5x + 3 \\
y = 1
\end{array}
\][/tex]
we start by recognizing that both equations equal [tex]\( y \)[/tex]. Therefore, we can set the expressions for [tex]\( y \)[/tex] from both equations equal to each other:
[tex]\[
-5x + 3 = 1
\][/tex]
Next, we solve for [tex]\( x \)[/tex] step-by-step:
1. Subtract 3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-5x = 1 - 3
\][/tex]
2. Simplify the right-hand side:
[tex]\[
-5x = -2
\][/tex]
3. Divide both sides by -5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-2}{-5} = 0.4
\][/tex]
Now that we have [tex]\( x = 0.4 \)[/tex], we substitute [tex]\( x \)[/tex] back into either of the original equations to find [tex]\( y \)[/tex]. We use the second equation since it's simpler:
[tex]\[
y = 1
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
(x, y) = (0.4, 1)
\][/tex]
So, the correct answer is:
[tex]\[
(0.4, 1)
\][/tex]
