Question

GG.1 Is (x, y) a solution to the system of equations?
N46
or
Is (1,4) a solution to this system of equations?
y=x+9
y=10x+7

Answer 1

To determine if the point \((1, 4)\) is a solution to the system of equations, we need to check whether it satisfies both equations:

1. **First equation**: \(y = x + 9\)
- Substitute \(x = 1\):
\[
y = 1 + 9 = 10
\]
- We found that when \(x = 1\), \(y\) should be \(10\). However, we have \(y = 4\) in the point \((1, 4)\), so this equation is not satisfied.

2. **Second equation**: \(y = 10x + 7\)
- Again, substitute \(x = 1\):
\[
y = 10(1) + 7 = 10 + 7 = 17
\]
- Here, when \(x = 1\), \(y\) should be \(17\). This again does not match, as we have \(y = 4\) in the point \((1, 4)\).

Since \((1, 4)\) does not satisfy either of the equations in the system, we conclude that:

\((1, 4)\) is **not** a solution to the system of equations.