To solve the given system of equations:
[tex]\[
\begin{array}{l}
y = -5x + 3 \\
y = 1
\end{array}
\][/tex]
we can proceed with the following steps:
1. Set the equations equal to each other: Since both expressions equal [tex]\( y \)[/tex], we can set the right-hand sides of the equations equal to each other.
[tex]\[
-5x + 3 = 1
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
- First, subtract 3 from both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[
-5x = 1 - 3
\][/tex]
[tex]\[
-5x = -2
\][/tex]
- Next, divide both sides of the equation by -5 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{-2}{-5}
\][/tex]
[tex]\[
x = 0.4
\][/tex]
3. Substitute [tex]\( x = 0.4 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]:
- We can substitute [tex]\( x = 0.4 \)[/tex] into the second equation [tex]\( y = 1 \)[/tex] because it's already simplified and directly gives the value of [tex]\( y \)[/tex].
[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]
