Question

A system of equations is graphed on a

coordinate plane.
Which coordinates are the best estimate of the
solution to the system of equations? {2x+3y=12 {4x+2y=10
(6,0)
(0,5)
(1,4)
(1,5)

Answer 1

Answer:1,

Explanation:

Answer 2

(1, 4)

Explanation:

`\text{It looks as if`

`\begin{array}{rcl}(1) & 2x + 3y = 12 & \\& 3y = 12 - 2x& \text{Subtracted 2x from each side}\\ & y = 4 - (2)/(3)x & \text{Divided each side by3}\\\\(2) & 4x + 2y =10& \\& 2y = 10 - 4x& \text{Subtracted 2x from each side}\\ & y = 5 - 2x & \text{Divided each side by 2}\\\end{array}\\`

Below are a few points for Equations (1) and (2).}

`\begin{array}cc\mathbf{x} & \mathbf{y} & \mathbf{x} & \mathbf{y}\\0 & 4 & 0 & 5\\& & 1 & 3\\& & 2 & 1\\3 & 2 & &\\6 & 0 & &\\\end{array}\\`

Equation (1) is the blue line in the graph below.

Equation (2) is the red line.

The two lines cross at the black dot

Your four points are labelled . The one that is closest to the intersection is (1, 4).

The approximate solution to the system of equations is (1, 4).