Which of the following ordered pairs is a solution to the equation 3x−2y=10%0D%0A3%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A10%0D%0A?(1 point)%0D%0AResponses%0D%0A%0D%0A(4,1)%0D%0A(%0D%0A4%0D%0A,%0D%0A1%0D%0A)%0D%0Aopen paren 4 comma 1 close paren%0D%0A%0D%0A(0,−3)%0D%0A(%0D%0A0%0D%0A,%0D%0A−%0D%0A3%0D%0A)%0D%0Aopen paren 0 comma negative 3 close paren%0D%0A%0D%0A(2,−1)%0D%0A(%0D%0A2%0D%0A,%0D%0A−%0D%0A1%0D%0A)%0D%0Aopen paren 2 comma negative 1 close paren%0D%0A%0D%0A(−3,2)
To determine which of the given ordered pairs is a solution to the equation, we substitute the values of x and y into the equation and check if the equation holds true.
Testing the first ordered pair, (4,1):
3(4) - 2(1) = 12 - 2 = 10 ------> The equation is satisfied.
Testing the second ordered pair, (0,-3):
3(0) - 2(-3) = 0 + 6 = 6 ------> The equation is not satisfied.
Testing the third ordered pair, (2,-1):
3(2) - 2(-1) = 6 + 2 = 8 ------> The equation is not satisfied.
Testing the fourth ordered pair, (-3,2):
3(-3) - 2(2) = -9 - 4 = -13 ------> The equation is not satisfied.
Therefore, the only ordered pair that is a solution to the equation is (4,1).