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 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]