Question

complete the table for the given system of linear equations. then, identify the ordered pair that satisfies the system of equations. \\(\

$$\begin{cases} y = 4x - 1 \\\\ y = -2x + 5 \\end{cases}$$

\\) \\(\boldsymbol{\cdot}\\) enter the answer in each space provided. use numbers instead of words. | \\(x\\) | \\(-2\\) | \\(-1\\) | \\(0\\) | \\(1\\) | \\(2\\) | |---|---|---|---|---|---| | \\(y = 4x - 1\\) | \\(-9\\) | \\(-5\\) | \\(-1\\) | \\(3\\) | \\(7\\) | | \\(y = -2x + 5\\) | \\(9\\) | \\(7\\) | \\(5\\) | \\(3\\) | \\(1\\) | the ordered pair \\(\left(\boxed{\quad}, \boxed{\quad}\
ight)\\) satisfies the system of equations.

Explanation:

Step1: Find x where y values match

We look at the table for \( y = 4x - 1 \) and \( y=-2x + 5 \). We check each \( x \) value:

• For \( x = -2 \): \( y = 4(-2)-1=-9 \) and \( y=-2(-2)+5 = 9 \) (not equal).
• For \( x=-1 \): \( y = 4(-1)-1=-5 \) and \( y=-2(-1)+5 = 7 \) (not equal).
• For \( x = 0 \): \( y = 4(0)-1=-1 \) and \( y=-2(0)+5 = 5 \) (not equal).
• For \( x = 1 \): \( y = 4(1)-1 = 3 \) and \( y=-2(1)+5 = 3 \) (equal).
• For \( x = 2 \): \( y = 4(2)-1 = 7 \) and \( y=-2(2)+5 = 1 \) (not equal).

Step2: Determine the ordered pair

Since at \( x = 1 \), both equations give \( y = 3 \), the ordered pair is \( (1, 3) \).

Answer:

\((1, 3)\)