Asked by Jim bob
Is (7, 3) the solution to the system of these linear equations: 3x+2y=5 and −x+6y=11? Why?
Answers
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Answered by
GPT-4o mini
To determine if the point (7, 3) is a solution to the system of equations \(3x + 2y = 5\) and \(-x + 6y = 11\), we need to substitute \(x = 7\) and \(y = 3\) into both equations and check if they hold true.
1. **Substituting into the first equation:**
\[
3x + 2y = 5
\]
Substituting \(x = 7\) and \(y = 3\):
\[
3(7) + 2(3) = 21 + 6 = 27
\]
Since \(27 \neq 5\), the first equation is not satisfied.
2. **Substituting into the second equation:**
\[
-x + 6y = 11
\]
Substituting \(x = 7\) and \(y = 3\):
\[
-7 + 6(3) = -7 + 18 = 11
\]
In this case, the second equation is satisfied.
Since the point (7, 3) does not satisfy the first equation, it is not a solution to the system of equations. Thus, the answer is **No**, (7, 3) is not a solution to the system.
1. **Substituting into the first equation:**
\[
3x + 2y = 5
\]
Substituting \(x = 7\) and \(y = 3\):
\[
3(7) + 2(3) = 21 + 6 = 27
\]
Since \(27 \neq 5\), the first equation is not satisfied.
2. **Substituting into the second equation:**
\[
-x + 6y = 11
\]
Substituting \(x = 7\) and \(y = 3\):
\[
-7 + 6(3) = -7 + 18 = 11
\]
In this case, the second equation is satisfied.
Since the point (7, 3) does not satisfy the first equation, it is not a solution to the system of equations. Thus, the answer is **No**, (7, 3) is not a solution to the system.
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