Solve the system of equations graphed below. (1 point) Responses (−1,3) open paren negative 1 comma 3 close paren (0,5) open paren 0 comma 5 close paren (5,−4) open paren 5 comma negative 4 close paren (3,−1)
To solve the system of equations graphed, we need to first write down the equations of the lines passing through the points provided.
Equation of the line passing through (-1, 3) and (0, 5):
Slope = (5 - 3) / (0 - (-1)) = 2 / 1 = 2
Using point-slope form: y - y1 = m(x - x1) where (x1, y1) = (-1, 3)
y - 3 = 2(x + 1)
y - 3 = 2x + 2
y = 2x + 5 ---(1)
Equation of the line passing through (0, 5) and (5, -4):
Slope = (-4 - 5) / (5 - 0) = -9 / 5
Using point-slope form: y - y1 = m(x - x1) where (x1, y1) = (0, 5)
y - 5 = -9/5(x - 0)
y - 5 = -9/5x
5y - 25 = -9x
9x + 5y - 25 = 0 ---(2)
Now, we can solve the system of equations (1) and (2) simultaneously to find the intersection point:
y = 2x + 5 ---(1)
9x + 5y - 25 = 0 ---(2)
Substitute y = 2x + 5 into (2):
9x + 5(2x + 5) - 25 = 0
9x + 10x + 25 - 25 = 0
19x = 0
x = 0
Substitute x = 0 into y = 2x + 5:
y = 2(0) + 5
y = 5
Therefore, the solution to the system of equations is (0, 5).