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You just studied 10 terms! x − y = 2 −−−−−−−−− ← add to and up with only 1 unknown 2x 0 = 8 Divide both sides by 2 Thus x = 4 '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ To determine value of y Substitute x = 4 into x y = 6 giving x y = 6 → 4 y = 6 Subtract 4 from both sides

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 Ex62, 5 Solve the given inequality graphically in twodimensional plane x – y ≤ 2 x – y ≤ 2 Lets first draw graph of x – y = 2 Drawing graph Checking for (0,0) Putting x = 0, y = 0 x – y ≤ 2 0 – 0 ≤ 2 0 ≤ 2 which is true Hence origin lies in the plane 3x 2y > 6Y=x2 y=2x2 (graph 300x0 pixels, x from 6 to 5, y from 10 to 10, of TWO functions y = x 2 and y = 2x 2) since y=x2 then we substitute (x2) for y in the other equation & solve for x x2=2x2 x2x=0 x=0 answer now substitute 0 for x & solve for y y=2*02 Solve the first equation for y Find the slope and yintercept Solve the second equation for y Find the slope and yintercept Graph the lines Determine the point of intersection The lines intersect at (−1, 2) Check the solution in both equations The solution is (−1, 2)

To find the yintercept Let x=0 in the equation, then solve for y The yintercept is ( 0, –2 ) Now we can plot the two points on the xy axis and connect them using a straight edge ruler to show the graph of the line Example 2 Graph the equation of the line using its intercepts This equation of the line is in the SlopeIntercept FormDraw the graph by joining the points by a smooth curve To find the roots of 2x2x−6=0, solve the two equations y=2x2 and 2x2x−6=0 Now, 2x2x−6=0 Hence, the roots of 2x2x−6=0 are nothing but the xcoordinates of the points of intersection of y=2x2 and y=−x6 Subtract both sides by 2;

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1 Solve the system by graphing or using a table Y=x2 y=2x7 2 Solve the system by graphing or using a table 2x4y=12 xy=2 Nice work!Step 2 Substitute the value of x into the other equation In this case the equation is 2x 3y = 1 Substituting (4 2y) for x, we obtain 2 (4 2y) 3y = 1, an equation with only one unknown The reason for this is that if x = 4 2y in one of the equations, then x

Incoming Term: x+y=2 solve and graph, solve x+y=2 graphically, x+y=-2 and 2x-y=8 solve graphically, solve x+y=2 and x-y=4 graphically,

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