To determine which of the given points is a solution to the system of equations
- \( y = \frac{2}{3}x - 5 \)
- \( y = \frac{7}{3}x - 1 \)
we will substitute each point into both equations and check if it satisfies both.
Check Point (−2.4,−6.6)
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For the first equation: \[ y = \frac{2}{3}(-2.4) - 5 = -1.6 - 5 = -6.6 \] This point satisfies the first equation.
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For the second equation: \[ y = \frac{7}{3}(-2.4) - 1 = -5.6 - 1 = -6.6 \] This point satisfies the second equation.
Since both equations are satisfied, (−2.4, −6.6) is a solution.
Check Point (2.4,−6.6)
- For the first equation: \[ y = \frac{2}{3}(2.4) - 5 = 1.6 - 5 = -3.4 \] This point does not satisfy the first equation.
Check Point (−2.4, 6.6)
- For the first equation: \[ y = \frac{2}{3}(-2.4) - 5 = -1.6 - 5 = -6.6 \] Does not equal 6.6.
Check Point (−1.2, 3.3)
- For the first equation: \[ y = \frac{2}{3}(-1.2) - 5 = -0.8 - 5 = -5.8 \] Does not equal 3.3.
After checking all points, the only point that satisfies both equations is:
(−2.4, −6.6).