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What is the solution to this system of equations?

[tex]\[
\left\{\begin{array}{l}
x+y=6 \\
x=y+4
\end{array}\right.
\][/tex]

A. [tex]\((1,5)\)[/tex]

B. [tex]\(\left(\frac{11}{2}, \frac{1}{2}\right)\)[/tex]

C. [tex]\(\left(\frac{21}{2}, \frac{11}{2}\right)\)[/tex]

D. [tex]\((5,1)\)[/tex]

Sagot :

GinnyAnsweridn
To determine the solution to the given system of equations, follow these steps carefully:

Given the system:
[tex]\[ \begin{cases} x + y = 6 \\ x = y + 4 \end{cases} \][/tex]

1. Substitute the second equation into the first:

Since [tex]\( x = y + 4 \)[/tex], we can substitute this expression for [tex]\( x \)[/tex] in the first equation.

Substitute [tex]\( x \)[/tex] in [tex]\( x + y = 6 \)[/tex]:
[tex]\[ (y + 4) + y = 6 \][/tex]

2. Simplify and solve for [tex]\( y \)[/tex]:

Combine like terms:
[tex]\[ y + 4 + y = 6 \][/tex]
[tex]\[ 2y + 4 = 6 \][/tex]

Isolate [tex]\( y \)[/tex] by first subtracting 4 from both sides:
[tex]\[ 2y = 2 \][/tex]

Then, divide by 2:
[tex]\[ y = 1 \][/tex]

3. Substitute [tex]\( y = 1 \)[/tex] back into the second equation to find [tex]\( x \)[/tex]:

Using [tex]\( x = y + 4 \)[/tex]:
[tex]\[ x = 1 + 4 \][/tex]
[tex]\[ x = 5 \][/tex]

4. Write the solution as an ordered pair:

The solution to the system is:
[tex]\[ (x, y) = (5, 1) \][/tex]

So, the correct solution to the system of equations is [tex]\((5, 1)\)[/tex]. Thus, the answer is:
[tex]\[ (5, 1) \][/tex]
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