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A coordinate graph goes from negative 10 to 10 in 1-unit increments on both the x- and y-axes. Two linear equations are graphed, along with four points.

The system of linear equations {y=3x+1y=−2x−4
is shown. Which of the points on the graph represents the solution to the linear system?

(1 point)
Responses

(0,1)
open paren 0 comma 1 close paren

(−2,3)
open paren negative 2 comma 3 close paren

(−1,−2)
open paren negative 1 comma negative 2 close paren

(0,−4)
open paren 0 comma negative 4 close paren
Remaining Attempts : 3
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1 answer

To determine which point represents the solution to the system of linear equations \(y = 3x + 1\) and \(y = -2x - 4\), we need to check which of the given points satisfies both equations.

Let's evaluate each point:

  1. For (0, 1):

    • Plugging \(x = 0\) into \(y = 3x + 1\): \(y = 3(0) + 1 = 1\) (True)
    • Plugging \(x = 0\) into \(y = -2x - 4\): \(y = -2(0) - 4 = -4\) (False) This point is NOT a solution.

  2. For (-2, 3):

    • Plugging \(x = -2\) into \(y = 3x + 1\): \(y = 3(-2) + 1 = -6 + 1 = -5\) (False)
    • Plugging \(x = -2\) into \(y = -2x - 4\): \(y = -2(-2) - 4 = 4 - 4 = 0\) (False) This point is NOT a solution.

  3. For (-1, -2):

    • Plugging \(x = -1\) into \(y = 3x + 1\): \(y = 3(-1) + 1 = -3 + 1 = -2\) (True)
    • Plugging \(x = -1\) into \(y = -2x - 4\): \(y = -2(-1) - 4 = 2 - 4 = -2\) (True) This point IS a solution.

  4. For (0, -4):

    • Plugging \(x = 0\) into \(y = 3x + 1\): \(y = 3(0) + 1 = 1\) (False)
    • Plugging \(x = 0\) into \(y = -2x - 4\): \(y = -2(0) - 4 = -4\) (True) This point is NOT a solution.

The point that represents the solution to the linear system is (-1, -2).