Explanation: Equation 1: 3 x − 2 y = 10 Equation 2 : 5 x + 2 y = 6 Both equations are in the standard form for a linear equation. This form makes it easy to determine the x- and y-intercepts. We can use those two points to graph each equation. X-intercept: value of x when y = 0 Substitute 0 for y and solve for x . Y-intercept: value of y when x = 0 Substitute 0 for x and solve for y . Equation 1 3 x − 2 y = 10 X-intercept: Substitute 0 for y and solve for x . 3 x − 2 ( 0 ) = 10 3 x = 10 Divide both sides by 3 . x = 10 3 or ≈ 3.333 x-intercept: ( 10 3 , 0 ) or ( ≈ 3.333 , 0 ) Plot this point. Y-intercept: Substitute 0 for x and solve for y . 3 ( 0 ) − 2 y = 10 − 2 y = 10 Divide both sides by − 2 . y = 10 − 2 y = − 5 y-intercept: ( 0 , − 5 ) Plot this point. Draw a straight line through the two points. This is the graph for Equation 1. Equation 2 5 x + 2 y = 6 X-intercept: Substitute 0 for y and solve for x . 5 x + 2 ( 0 ) = 6 5 x = 6 Divide both sides by 5 . x = 6 5 or 1.2 x-intercept: ( 6 5 , 0 ) or ( 1.2 , 0 ) Plot this point. Y-intercept: Substitute 0 for x and solve for y . 5 ( 0 ) + 2 y = 6 2 y = 6 Divide both sides by 2 . y = 6 2 y = 3 y-intercept: ( 0 , 3 ) Plot this point. Draw a line between the two points. This is the graph of Equation 2. The lines intersect at a single point, therefore the system of equations is consistent. graph{(3x-2y-10)(5x+2y-6)=0 [-10, 10, -5, 5]}
