A system of equations is graphed on acoordinate plane.Which coordinates are the best estimate of thesolution to the system of equations? {2x+3y=12 {4x+2y=10(6,0)(0,5)(1,4)(1,5)

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 dotYour 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).