Example 1 4 x 6 y 6 y 2 3 x 1 2 2 x 3 y 5 y 2 3 x 5 3 Math 17 UP IMath Systems

Example 1 4 x 6 y 6 y 2 3 x 1 2 2 x 3 y 5 y 2 3 x 5 3

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Example: ` 1 : 4 x + 6 y = 6 , y = - 2 3 x + 1 ` 2 : 2 x + 3 y = 5 , y = - 2 3 x + 5 3 Math 17 (UP-IMath) Systems Lec 12 15 / 29
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Two Lines In a system of two linear equations in two variables, if the lines representing the equations.. ..are parallel lines, then the system has no solution and is said to be inconsistent . Example: ` 1 : 4 x + 6 y = 6 , y = - 2 3 x + 1 ` 2 : 2 x + 3 y = 5 , y = - 2 3 x + 5 3 9 > > = > > ; Parallel. Math 17 (UP-IMath) Systems Lec 12 15 / 29
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Two Lines In a system of two linear equations in two variables, if the lines representing the equations.. ..coincide, then there are infinitely many solutions to the system. The system is said to be dependent . Math 17 (UP-IMath) Systems Lec 12 16 / 29
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Two Lines In a system of two linear equations in two variables, if the lines representing the equations.. ..coincide, then there are infinitely many solutions to the system. The system is said to be dependent . Ex. ` 1 : 4 x + 6 y = 6 ` 2 : 2 x + 3 y = 3 Math 17 (UP-IMath) Systems Lec 12 16 / 29
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Two Lines In a system of two linear equations in two variables, if the lines representing the equations.. ..coincide, then there are infinitely many solutions to the system. The system is said to be dependent . Ex. ` 1 : 4 x + 6 y = 6 , y = - 2 3 x + 1 ` 2 : 2 x + 3 y = 3 , y = - 2 3 x + 1 Math 17 (UP-IMath) Systems Lec 12 16 / 29
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Two Lines In a system of two linear equations in two variables, if the lines representing the equations.. ..coincide, then there are infinitely many solutions to the system. The system is said to be dependent . Ex. ` 1 : 4 x + 6 y = 6 , y = - 2 3 x + 1 ` 2 : 2 x + 3 y = 3 , y = - 2 3 x + 1 9 > > = > > ; Same line. Math 17 (UP-IMath) Systems Lec 12 16 / 29
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Two Lines In a system of two linear equations in two variables, if the lines representing the equations.. ..coincide, then there are infinitely many solutions to the system. The system is said to be dependent . Ex. ` 1 : 4 x + 6 y = 6 , y = - 2 3 x + 1 ` 2 : 2 x + 3 y = 3 , y = - 2 3 x + 1 9 > > = > > ; Same line. Note: A system of two linear equations is dependent if one equation can be obtained by multiplying both sides of the other by a nonzero constant. Math 17 (UP-IMath) Systems Lec 12 16 / 29
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A Line and a Parabola Ex. Find the points of intersection of the graphs of p : y = x 2 - 4 x + 2 and ` : y = 2 x - 3 Math 17 (UP-IMath) Systems Lec 12 17 / 29
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A Line and a Parabola Ex. Find the points of intersection of the graphs of p : y = x 2 - 4 x + 2 and ` : y = 2 x - 3 Solution: By Substitution Method, Math 17 (UP-IMath) Systems Lec 12 17 / 29
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A Line and a Parabola Ex. Find the points of intersection of the graphs of p : y = x 2 - 4 x + 2 and ` : y = 2 x - 3 Solution: By Substitution Method, 2 x - 3 = x 2 - 4 x + 2 (Take value of y in ` and replace y in p ) Math 17 (UP-IMath) Systems Lec 12 17 / 29
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A Line and a Parabola Ex. Find the points of intersection of the graphs of p : y = x 2 - 4 x + 2 and ` : y = 2 x - 3 Solution: By Substitution Method, 2 x - 3 = x 2 - 4 x + 2 (Take value of y in ` and replace y in p ) ) 0 = x 2 - 6 x + 5 (Solve for x ) Math 17 (UP-IMath) Systems Lec 12 17 / 29
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A Line and a Parabola Ex. Find the points of intersection of the graphs of p : y = x 2 - 4 x + 2 and ` : y = 2 x - 3 Solution: By Substitution Method, 2 x - 3 = x 2 - 4 x + 2 (Take value of y in ` and replace y in p ) ) 0 = x 2 - 6 x + 5 (Solve for x ) 0 = ( x - 1)( x - 5) Math 17 (UP-IMath) Systems Lec 12 17 / 29
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A Line and a Parabola Ex. Find the points of intersection of the graphs of p : y = x 2 - 4 x + 2 and ` : y = 2 x - 3
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