The boundary of a linear inequality is 3x+2y= 12. The coordinates (2, 3) satisfies the inequality, so
A. a dashed line will represent the boundary, but the solution region is unknown
B. a solid line will represent the boundary, but the solution region is unknown
C. the boundary line type is unknown, but the solution region is above the
boundary
D. the boundary line type is unknown, but the solution region is below the
boundary
I wanna say A but im not 100 percent sure
3*2 + 2*3 = 12 which lies on the line.
so the boundary is a solid line.
So B
To determine whether the boundary of the linear inequality 3x + 2y = 12 should be represented by a dashed or solid line, you need to consider the inequality sign.
Since the equation 3x + 2y = 12 is an equality (not an inequality), the boundary line will be represented by a solid line.
Now, since the coordinates (2, 3) satisfy the inequality, you need to substitute these values into the inequality to see if it is true.
Substituting the values x = 2 and y = 3 into the equation 3x + 2y = 12:
3(2) + 2(3) = 6 + 6 = 12
Since the equation is true, the solution lies on the boundary line. Therefore, the solution region is below the boundary.
Therefore, the correct answer is D. The boundary line type is unknown, but the solution region is below the boundary.