What is the solution to the system of equations?

[tex]\[
\begin{array}{l}
y = -5x + 3 \\
y = 1
\end{array}
\][/tex]

A. [tex]\((0.4, 1)\)[/tex]
B. [tex]\((0.8, 1)\)[/tex]
C. [tex]\((1, 0.4)\)[/tex]
D. [tex]\((1, 0.8)\)[/tex]



Answer :

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]