Solve the system of equations graphed below.
(1 point)
Responses
(0,5)
open paren 0 comma 5 close paren
(−1,3)
open paren negative 1 comma 3 close paren
(5,−4)
open paren 5 comma negative 4 close paren
(3,−1)
open paren 3 comma negative 1 close paren
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The system of equations graphed below can be solved by finding the point where the two lines intersect:
The equations of the lines are:
- Line 1: y = 2x + 5
- Line 2: y = -x - 2
To find the point of intersection, set the equations equal to each other:
2x + 5 = -x - 2
Now, solve for x:
3x = -7
x = -7/3
Substitute x back into one of the equations to solve for y:
y = -(-7/3) - 2
y = 7/3 - 2
y = 1/3
Therefore, the point of intersection is (-7/3, 1/3).