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There are several ways to solve systems of equations There are several ways to solve systems of equations Graphing There are several ways to solve systems of equations Graphing Substitution There are several ways to solve systems of equations Graphing Substitution Elimination There are several ways to solve systems of equations This lesson will deal with substitution Graphing Substitution Elimination When given a system of equations When given a system of equations y = 2x - 5 x + y = 4 When given a system of equations You can solve for x and y by substituting y = 2x - 5 x + y = 4 When given a system of equations You can solve for x and y by substituting Notice the second equation y = 2x - 5 x + y = 4 When given a system of equations You can solve for x and y by substituting Notice the second equation y = 2x - 5 x + y = 4 second equation When given a system of equations You can solve for x and y by substituting Notice the second equation The y is by itself y = 2x - 5 x + y = 4 When given a system of equations You can solve for x and y by substituting Notice the second equation The y is by itself y = 2x - 5 x + y = 4 y by itself When given a system of equations You can solve for x and y by substituting Notice the second equation The y is by itself That means 2x - 5 is the exact same as y y = 2x - 5 x + y = 4 2x - 5 When given a system of equations You can solve for x and y by substituting Notice the second equation The y is by itself That means 2x - 5 is the exact same as y So we can substitue a 2x - 5 anywhere we see a y y = 2x - 5 x + y = 4 Fill in the blank We see a y in the first equation y = 2x - 5 x + y = 4 We see a y in the first equation y = 2x - 5 x + y = 4 a 'y' We see a y in the first equation so we can replace that y with a 2x - 5 y = 2x - 5 x + y = 4 a 'y' We see a y in the first equation so we can replace that y with a 2x - 5 y = 2x - 5 x + (2x - 5) = 4 put a 2x - 5 in for y What can we put for y? We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 new equation We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 new equation x + (2x - 5) = 4 We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 new equation x + (2x - 5) = 4 x + 2x - 5 = 4 We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 new equation x + (2x - 5) = 4 x + 2x - 5 = 4 3x - 5 = 4 We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 new equation x + (2x - 5) = 4 x + 2x - 5 = 4 3x - 5 = 4 3x = 9 We see a y in the first equation so we can replace that y with a 2x - 5 and we can solve our new equation y = 2x - 5 x + (2x - 5) = 4 new equation x + (2x - 5) = 4 x + 2x - 5 = 4 Find the value for x 3x - 5 = 4 3x = 9 x = 3 So now we know x is 3 y = 2x - 5 x + y = 4 x = 3 So now we know x is 3 But we have to find y y = 2x - 5 x + y = 4 x = 3 So now we know x is 3 But we have to find y y = 2x - 5 x + y = 4 x = 3 y = ? So now we know x is 3 But we have to find y We do that by putting 3 in for x y = 2x - 5 x + y = 4 x = 3 y = ? So now we know x is 3 But we have to find y We do that by putting 3 in for x Let's use the second equation (we can use either) y = 2x - 5 x + y = 4 x = 3 y = ? So now we know x is 3 But we have to find y We do that by putting 3 in for x Let's use the second equation (we can use either) y = 2(3) - 5 x + y = 4 put 3 in for x What do you put in for x? x = 3 y = ? So now we know x is 3 But we have to find y We do that by putting 3 in for x Let's use the second equation (we can use either) y = 2(3) - 5 = 1 x + y = 4 and solve x = 3 y = ? So now we know x is 3 But we have to find y We do that by putting 3 in for x So we know that y = 1 Let's use the second equation (we can use either) y = 2(3) - 5 = 1 x + y = 4 and solve x = 3 y = ? So now we know x is 3 But we have to find y We do that by putting 3 in for x So we know that y = 1 Let's use the second equation (we can use either) y = 2(3) - 5 = 1 x + y = 4 and solve What does y equal? x = 3 y = 1 so that's our answer y = 2x - 5 x + y = 4 x = 3 y = 1 |