Question

Determine whether the given point is a solution to the system of equations.Help please! Explain

A.(2,-5)

x+y=-3

2x-y=6

B. (1,-4
X+y=-3
2x-y=6

Answer 1

Answer:

A:  Yes; B:  Yes

Step-by-step explanation:

Is (2, -5) a solution of this System A?

Substituting 2 for x in x + y = -3 yields 2 + y = -3.  Solving this for y yields:

y = -3 - 2 = -5.  Yes, (2, -5) is a solution of this System A.

Is (1, -4) a solution of the system

x + y = -3

2x - y = 6

Check this out by substituting 1 for x and -4 for y in the above.  We get

1 - 4 = -3, which satisfies the first equation.

Substituting 1 for x and -4 for y in the second equation results in 2 - (-4) = 6, which is true.

In both cases A and B, the given possible solution has been shown to be correct.

Answer 2

Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.