Jian made a table showing some x- and y-values in a system of equations. Use his table to identify the solution for the system. (1 point) Responses
(3,0)
(2,−1)
There is an infinite number of solutions.
There is no solution.
To identify the solution for the system, we need to substitute the x- and y-values into the equations and check if they satisfy both equations.
Let's examine the given options:
(3,0)
Substituting x=3 and y=0 into the equations:
Equation 1: 2x + y = 6
2(3) + 0 = 6
6 = 6 (satisfied)
Equation 2: x - y = 3
3 - 0 = 3
3 = 3 (satisfied)
(2,−1)
Substituting x=2 and y=-1 into the equations:
Equation 1: 2x + y = 6
2(2) + (-1) = 6
4 - 1 = 6
3 ≠ 6 (not satisfied, as 3 is not equal to 6)
Equation 2: x - y = 3
2 - (-1) = 3
2 + 1 = 3
3 = 3 (satisfied)
Based on these calculations, only (3,0) satisfies both equations, so the solution for the system is (3,0). Thus, the correct response is: (3,0).