A system of equations is shown:

[tex]\[
\begin{array}{l}
2x = -y + 6 \\
-4x + 3y = 8
\end{array}
\][/tex]

What is the solution to this system of equations?

A. [tex]\((-1, -4)\)[/tex]
B. [tex]\((1, 4)\)[/tex]
C. [tex]\((4, 1)\)[/tex]
D. [tex]\((-4, -1)\)[/tex]



Answer :

To find the solution to the given system of equations, we can use a method such as substitution or elimination. Here, we'll use the substitution method for the detailed step-by-step solution.

We start with the given system of equations:

[tex]\[ \begin{array}{l} 2x = -y + 6 \\ -4x + 3y = 8 \end{array} \][/tex]

### Step 1: Solve the first equation for [tex]\( y \)[/tex]:

First, solve the first equation for [tex]\( y \)[/tex]:

[tex]\[ 2x = -y + 6 \][/tex]

Add [tex]\( y \)[/tex] to both sides:

[tex]\[ 2x + y = 6 \][/tex]

Subtract [tex]\( 2x \)[/tex] from both sides to isolate [tex]\( y \)[/tex]:

[tex]\[ y = 6 - 2x \][/tex]

### Step 2: Substitute [tex]\( y \)[/tex] in the second equation:

Now substitute [tex]\( y = 6 - 2x \)[/tex] into the second equation:

[tex]\[ -4x + 3y = 8 \][/tex]

Replace [tex]\( y \)[/tex] with [tex]\( 6 - 2x \)[/tex]:

[tex]\[ -4x + 3(6 - 2x) = 8 \][/tex]

### Step 3: Simplify and solve for [tex]\( x \)[/tex]:

Expand the equation:

[tex]\[ -4x + 18 - 6x = 8 \][/tex]

Combine like terms:

[tex]\[ -10x + 18 = 8 \][/tex]

Subtract 18 from both sides to isolate the term with [tex]\( x \)[/tex]:

[tex]\[ -10x = 8 - 18 \][/tex]

[tex]\[ -10x = -10 \][/tex]

Divide both sides by [tex]\(-10\)[/tex]:

[tex]\[ x = 1 \][/tex]

### Step 4: Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]:

Now substitute [tex]\( x = 1 \)[/tex] back into the equation [tex]\( y = 6 - 2x \)[/tex]:

[tex]\[ y = 6 - 2(1) \][/tex]

[tex]\[ y = 6 - 2 \][/tex]

[tex]\[ y = 4 \][/tex]

### Conclusion:

The solution to the system of equations is [tex]\( x = 1 \)[/tex] and [tex]\( y = 4 \)[/tex]. Therefore, the point [tex]\((1, 4)\)[/tex] is the solution.

From the given options, we can see that the correct answer is:

[tex]\[ (1, 4) \][/tex]