A pair of equations is shown below. X + Y = 2 Y= 1/2x + 5 If the two equations are graphed, at what point do the lines representing the two equations intersect?

Question

asked Jun 10, 2024 202k views

1 Answer

Jeferson Macedo · Answer 1 · 2024-06-14T23:41:55+0000

To find the point of intersection between the two lines represented by the given equations, we can solve the system of equations simultaneously.

The given equations are:

1) X + Y = 2

2) Y = (1/2)X + 5

We can solve this system by substituting the value of Y from the second equation into the first equation. Let's proceed with the substitution method:

Substitute Y = (1/2)X + 5 into the first equation:

X + (1/2)X + 5 = 2

Combine like terms:

(3/2)X + 5 = 2

Subtract 5 from both sides:

(3/2)X = -3

Multiply both sides by 2/3 to isolate X:

X = -2

Now, substitute the value of X back into the second equation to find Y:

Y = (1/2)(-2) + 5

Y = -1 + 5

Y = 4

Therefore, the lines represented by the given equations intersect at the point (-2, 4).