Asked by Michael Bergamo on Jun 10, 2024
Verified
Solve the system of linear equations below by any convenient method. {2x−2y=2−2x+y=−2\left\{ \begin{array} { c } 2 x - 2 y = 2 \\- 2 x + y = - 2\end{array} \right.{2x−2y=2−2x+y=−2
A) (-2,-1)
B) (-1,0)
C) (1,0)
D) (3,-1)
E) (2,1)
Linear Equations
Equations that depict lines in a coordinate system and can be written in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
System
A set of principles or procedures according to which something is done; in mathematics, often refers to a set of equations or inequalities.
Elimination
A method used in algebra to solve systems of equations by removing variables to find their values.
- Solve systems of linear equations using different methods.
Verified Answer
SM
Sofia MartinezJun 13, 2024
Final Answer :
C
Explanation :
Multiply the second equation by 2 and add the two equations to eliminate $x$:
2x−2y=2−4x+2y=−4\begin{align*}2x-2y&=2 \\-4x+2y&=-4 \\\end{align*}2x−2y−4x+2y=2=−4
Adding yields $-2x=-2$, or $x=1$. Substituting into the second equation gives $y=0$. Therefore, the solution is $(1,0)$, which is choice $\boxed{\textbf{(C)}}$.
2x−2y=2−4x+2y=−4\begin{align*}2x-2y&=2 \\-4x+2y&=-4 \\\end{align*}2x−2y−4x+2y=2=−4
Adding yields $-2x=-2$, or $x=1$. Substituting into the second equation gives $y=0$. Therefore, the solution is $(1,0)$, which is choice $\boxed{\textbf{(C)}}$.
Learning Objectives
- Solve systems of linear equations using different methods.