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GG.1 Is (x, y) a solution to the system of equations?

N46
Is (7,
–
2) a solution to this system of equations?
x–5y=
–
3
y=
–
2

1 answer

To determine if the point \((7, -2)\) is a solution to the system of equations, we'll substitute \(x = 7\) and \(y = -2\) into each equation.

The system of equations is:

  1. \(x - 5y = -3\)
  2. \(y = -2\)

Check the second equation first:

Substituting \(y = -2\) into the second equation: \[ y = -2 \] This is true, so \((7, -2)\) satisfies the second equation.

Now check the first equation:

Substituting \(x = 7\) and \(y = -2\) into the first equation: \[ 7 - 5(-2) = -3 \] Calculating the left side: \[ 7 - 5(-2) = 7 + 10 = 17 \] Now we compare: \[ 17 \neq -3 \] Thus, the first equation is not satisfied.

Conclusion:

Since \((7, -2)\) does not satisfy the first equation, \((7, -2)\) is not a solution to the system of equations.