Answer:
(1, 4)
Step-by-step explanation:
[tex]\text{It looks as if "they" are asking you to solve the problem graphically.}\\\text{Then, you must solve each equation for y, plot a few points for each graph,}\\ \text{and see where each graph intersects. }[/tex]
[tex]\begin{array}{rcl}(1) & 2x + 3y = 12 & \\& 3y = 12 - 2x& \text{Subtracted 2x from each side}\\ & y = 4 - \dfrac{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}\\[/tex]
Below are a few points for Equations (1) and (2).}
[tex]\begin{array}{cc|cc}\mathbf{x} & \mathbf{y} & \mathbf{x} & \mathbf{y}\\0 & 4 & 0 & 5\\& & 1 & 3\\& & 2 & 1\\3 & 2 & &\\6 & 0 & &\\\end{array}\\[/tex]
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).
