Question

Which system (s) of linear equations has (have ) (3,-2) as its (their ) unique solution? Select ALL that apply.

A)y=-2,x=3
B)y=4x-14,y=-x+1
C)y=3,x=-2
D)y=-3x+7,y=x-5
E)y=-3x-5,y=2x+1

Answer 1

After substituting the point (3, -2) into each system of equations, it's determined that systems A, B, and D have (3, -2) as their unique solution, while systems C and E do not.

Step-by-step explanation:

To find which system(s) of linear equations have (3, -2) as their unique solution, we substitute x = 3 and y = -2 into each system.

• For system A, y = -2, x = 3, clearly this system has (3, -2) as its unique solution.
• For system B, substituting the point (3, -2) into the equations gives: y = 4x - 14 becomes -2 = 4(3) - 14, which is true; and y = -x + 1 becomes -2 = -(3) + 1, which is also true. Hence, system B also has (3, -2) as a solution.
• System C y = 3, x = -2 does not satisfy the point (3, -2).
• For system D, substituting gives us y = -3x + 7 which becomes -2 = -3(3) + 7, which is true, and y = x - 5 becomes -2 = 3 - 5, which is also true. Thus, system D also has (3, -2) as its unique solution.
• Finally, substituting into system E's equations: y = -3x - 5 and y = 2x + 1 does not give us correct equalities when x=3 and y=-2. Therefore, system E does not have (3, -2) as its solution.

Therefore, the systems that have (3, -2) as their unique solution are A, B, and D.