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 :

Let's solve the system of equations to find the intersection point:

We are given the following system of equations:
[tex]\[ \begin{array}{l} y = -5x + 3 \\ y = 1 \end{array} \][/tex]

To find the solution, we need to determine the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.

Step 1: Set the two equations equal to each other, since they both equal [tex]\(y\)[/tex]:
[tex]\[ -5x + 3 = 1 \][/tex]

Step 2: Solve for [tex]\(x\)[/tex]:

Subtract 3 from both sides of the equation:
[tex]\[ -5x + 3 - 3 = 1 - 3 \][/tex]
[tex]\[ -5x = -2 \][/tex]

Divide both sides by -5:
[tex]\[ x = \frac{-2}{-5} \][/tex]
[tex]\[ x = \frac{2}{5} \][/tex]

So, [tex]\(x = \frac{2}{5}\)[/tex].

Step 3: Substitute [tex]\(x = \frac{2}{5}\)[/tex] back into the second original equation to find [tex]\(y\)[/tex]. However, since the second equation is [tex]\(y = 1\)[/tex], we know that [tex]\(y = 1\)[/tex].

Therefore, the solutions are:
[tex]\[ x = \frac{2}{5} \quad \text{and} \quad y = 1 \][/tex]

Thus, the solution to the system of equations is [tex]\(\left(\frac{2}{5}, 1\right)\)[/tex].

Since [tex]\(\frac{2}{5} = 0.4\)[/tex], the solution in decimal form is [tex]\((0.4, 1)\)[/tex].

So, the correct choice from the given options is:
[tex]\[ (0.4, 1) \][/tex]