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Verify if (5/3,-2/3) is a solution to the system of equations y=1/2x-3/2 and y=-x+1

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4 votes

Final answer:

After substituting the x-value of the point (5/3,-2/3) into both equations, we find that it results in the y-value of -2/3 for each equation. Hence, the point (5/3,-2/3) is a solution to the system of equations.

Step-by-step explanation:

To verify if the point (5/3,-2/3) is a solution to the system of equations y=1/2x-3/2 and y=-x+1, we need to check whether the point satisfies both equations.

For the first equation:

Substitute x = 5/3 into y = 1/2x - 3/2:

y = (1/2)(5/3) - 3/2 = 5/6 - 3/2 = 5/6 - 9/6 = -4/6 = -2/3

For the second equation:

Substitute x = 5/3 into y = -x + 1:

y = -(5/3) + 1 = -5/3 + 3/3 = -2/3

Since the point gives a value of y = -2/3 in both equations, the point (5/3,-2/3) is indeed a solution to the system of equations.

User Thijs Riezebeek
by
8.7k points
2 votes
(5/3)(1/2) - 3/2 = 5/6 - 9/6 = -4/6 = -2/3 check
5/3 +1 = 5/3+3/3 = 8/3 NOPE. Not a solution.
User Felix Aballi
by
7.8k points

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