Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

On your own paper, solve the system of equations using substitution and identify the solution.

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

A. (6, 4)
B. (4, 2)
C. (2, 0)
D. (8, 6)
E. No Solution
F. Infinitely Many Solutions

Sagot :

GinnyAnswer
To solve the system of equations using substitution, we will follow these steps:

1. Solve one of the equations for one variable:
[tex]\[ x - 2 = y \][/tex]
Solve this for [tex]\( y \)[/tex]:
[tex]\[ y = x - 2 \][/tex]

2. Substitute [tex]\( y = x - 2 \)[/tex] into the second equation:
[tex]\[ -2x + 2y = 2 \][/tex]
Replace [tex]\( y \)[/tex] in the second equation with [tex]\( x - 2 \)[/tex]:
[tex]\[ -2x + 2(x - 2) = 2 \][/tex]
Simplify the equation:
[tex]\[ -2x + 2x - 4 = 2 \][/tex]
The [tex]\( -2x \)[/tex] and [tex]\( 2x \)[/tex] cancel each other out:
[tex]\[ -4 = 2 \][/tex]
This statement is false, which means the system of equations is inconsistent.

Since the system of equations is inconsistent, there are no solutions that satisfy both equations.

Therefore, the answer to the system given is:

[tex]\[ \boxed{\text{No Solution}} \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.