Answered

Discover a wealth of knowledge and get your questions answered on IDNLearn.com. Discover in-depth and trustworthy answers from our extensive network of knowledgeable 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 :

GinnyAnsweridn
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]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.