Question

Systems of linear equations online practice
Is (5,-1) a solution to the system of these linear equations c+y=4 and 2x +3y=7? Why?

Answer 1

To determine if the point (5, -1) is a solution to the system of equations given by \(c + y = 4\) and \(2x + 3y = 7\), we will substitute \(x = 5\) and \(y = -1\) into both equations.

1. For the first equation \(c + y = 4\), it seems like there might be a typo or unclear notation because it uses the variable \(c\) instead of \(x\). If we assume the equation is actually \(x + y = 4\), then we can substitute:

\[
5 + (-1) = 4
\]
\[
4 = 4 \quad \text{(True)}
\]

2. Now, let's check the second equation \(2x + 3y = 7\):

\[
2(5) + 3(-1) = 7
\]
\[
10 - 3 = 7
\]
\[
7 = 7 \quad \text{(True)}
\]

Since both equations are satisfied by the point (5, -1), we conclude that (5, -1) **is** a solution to the system of equations (assuming the first equation was meant to be \(x + y = 4\)). If the first equation was indeed supposed to contain a variable \(c\), we would need clarification on its context.