Question
\( \left. \begin{array} { l l l } { x + 2 = y } & { \rightarrow } & { y = x + 2 } \\ { y - x = - 3 } & { \rightarrow } & { y = \square } \end{array} \right. \)
Ask by Edwards Lawson. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There is no solution to the system of equations.
Solution
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}x+2=y\\y-x=-3\end{array}\right.\)
- step1: Rewrite the expression:
\(\left\{ \begin{array}{l}y=x+2\\y-x=-3\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(x+2-x=-3\)
- step3: Simplify:
\(2=-3\)
- step4: Calculate:
\(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\)
- step5: Rewrite:
\((x, y) \in \varnothing\)
The system of equations given is:
1. \( x + 2 = y \)
2. \( y - x = -3 \)
Let's analyze these equations step by step.
1. From the first equation, we can express \( y \) in terms of \( x \):
\[
y = x + 2
\]
2. Now, substituting this expression for \( y \) into the second equation:
\[
(x + 2) - x = -3
\]
3. Simplifying this gives:
\[
2 = -3
\]
This statement is false, indicating that there is no solution to the system of equations. Therefore, the final conclusion is:
**No solution**.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
Did you know that this system of equations can represent a straight line on a graph? The first equation, \( y = x + 2 \), is a line with a y-intercept of 2, meaning it crosses the y-axis at that point. The second equation can be rearranged to find its slope and intercept too! To find \( y \) in the second equation \( y - x = -3 \), simply add \( x \) to both sides, giving us \( y = x - 3 \). Now you have two linear equations to work with! You can solve them together to find their intersection point, which tells you where the two lines meet on the graph.
