# SOLUTION: I cannot figure out how to solve systems by graphing. I have read and read but am so confused. I need to solve the system 2x+y=2; 6x+4y=12. Please help me figure out the answer

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 Click here to see ALL problems on Linear-systems Question 632161: I cannot figure out how to solve systems by graphing. I have read and read but am so confused. I need to solve the system 2x+y=2; 6x+4y=12. Please help me figure out the answer and show/explain how. Thanks.Found 2 solutions by josmiceli, ewatrrr:Answer by josmiceli(9817)   (Show Source): You can put this solution on YOUR website!You have 2 straight lines. The best way to get an idea what they look like is to convert the equations from the standard form ( as they now are ) into the slope-intercept form --------------------- (1) and (2) --------------------- (1) and (2) are now in the form where = slope and = y - intercept --------------------- In (1), In (2), Both slope are negative, which means they go from upper left to lower right on the graph, opposite to what a positive slope does --------------------- gives you a point for free on each line. It is the y-intercept point which is (0,b), or (0, 2) for equation (1) (0,6) for equation (2) -------------------- Now you just need 1 other point for both lines, and since 2 points determine a line, you can draw each line. Where the lines intersect is the solution to the system of lines -------------------- To find the other point, just plug in any value for , and read off the value for For example: (1) I'll pick (1) (1) So, I have the point (1,0) and (2) I'll pick (2) (2) (2) So, I have the point (2,0) --------------------- Now you have this information about the lines: Line (1): (0,2) (1,0) ---------- Line (2): (0,6) (2,0) ---------- And that's all you need Answer by ewatrrr(10682)   (Show Source): You can put this solution on YOUR website! ``` Hi, Solve the system by putting each of their graphs on the same graph the point they intersect at: (-2,6) is the solution for this system If You are having difficulty graphing each of the linear equations: find at least 2 (x,y)points for each and connect pair of the 2 points with their respective line 2x+y=2 x = 0 ⇒ y = 2, y = 0 ⇒ x = 1 (0,2) and (1,0) on this line 6x+4y=12 x = 0 ⇒ y= 3, y = 0 ⇒ x = 2 (0,3) and (2,0) on this line ```