Question
a) \( x+y=5 ; \quad x-y=3 \)
Ask by Mccarthy Greene. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( x = 4 \) and \( y = 1 \).
Solution
1. We start with the system of equations:
\[
x + y = 5
\]
\[
x - y = 3
\]
2. Adding the two equations, we get:
\[
(x + y) + (x - y) = 5 + 3
\]
\[
2x = 8
\]
\[
x = 4
\]
3. Substitute \( x = 4 \) into the first equation:
\[
4 + y = 5
\]
\[
y = 1
\]
4. The solution to the system is:
\[
x = 4,\quad y = 1
\]
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Simplify this solution Extra Insights
To solve these equations, we can use the substitution or elimination method. Let’s use elimination here. Adding both equations together eliminates \(y\): \[ (x + y) + (x - y) = 5 + 3 \] This simplifies to \(2x = 8\), giving us \(x = 4\). Now, substituting \(x = 4\) back into the first equation: \[ 4 + y = 5 \] This leads to \(y = 1\). So the solution is \(x = 4\) and \(y = 1\). Now, if you were to visualize this, you could graph both equations. The intersection point where both lines cross is where your solution lies! In our case, it would be the point (4, 1), giving a lovely geometric representation of the algebra we just solved.
