Week 7 notes - To solve a system of two equations in two...

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To solve a system of two equations in two variables, find all ordered pairs, if any, which are solutions of both equations. **The graph of a linear equation in two variables is a straight line.** When a line intersects the y-axis what is the value of x?= 0 A system of equations is consistent if it has at least one solution. If it has no solution it is inconsistent. The equations are dependent if the system has infinitely many solutions. If it has exactly one solution or no solution it is independent. Solve the system of equations by graphing. Then classify the system X+y=15 x-y= 1 x+y=15 if x=6 then 6+y=15 Y=9 (6,9) X+y=15 If y=5 then X+5=15 X=10 (10,5) x-y=1 if x =0 then 0-y=1 Y=-1 (0,-1) x-y=1 y=0 then x-0=1 x=-1 (1,0) The solution of the system is: (8,7) The system is consistent The equations are independent Solve the system of equations by graphing. Then classify the system. 2x-y=18 2x+3y=2 2x-y=18 If x=8 then 16-y=18 Y=-2 (8,-2) 2x-y=18 If y=-6 then 2x-(-6)=18 X=6 (6,-6) 2x+3y=2 If X=0 then 3y=2 Y= 2/3 =.66 (0,2/3) 2x+3y=2 If Y=0 then 2x=2 X=1 (1,0)
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The solution is (7,-4) The system is consistent The equations are independent Solve the system of equations by graphing. Then classify the system 6u+v=11 6u=v+25 (U= x, V=y) 6u+v=11 If U = 1 then 6+v=11 V= 5 (1,5) 6u+v=11 If V=-1 then 6u=-1=11 U=2 (2,-1) 6U=V+25 If U=0 then V+25 -25=V (0,-25) 6U=V+25 If V=0 then 6U=25 (25,0) The solution is (3,-7) The system is consistent The equations are independent Solve the system of equations by graphing. Then classify the system Y= -x-9 4x-3y= -15 Y= -x-9 If Y=-2 then -2= -x-9 X= -9+2 X= -7 (-7,2) Y= -x-9 If X=4 then Y= -4-9 Y= -13 (4,-13) 4x-3y=15 If X=0 then -3y=15 Y= -5 (0,-5) 4x-3y=15 If Y=0 then 4x=15 X= 15/4= 3.75 (3.75,0) The solution is (-6,-3) The system is consistent The equations are independentSolve by the SUBSTITUTION method
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6x-8y= -12 3x+24=y The 1 st step is to solve an equation for one variable. If the coefficient of a variable is 1 or -1, it is easier to solve for that variable. The 2 nd equation is already solved for y so it is easiest to use. Next, substitute (3x+24) for y into the other original equation. Remember to use parentheses when you substitute. Then remove them carefully. Substitute (3x+24) for y 6x-8(3x+24) = -12 Use the distributive law 6x-24x-192= -12 Collect like terms-18x=180 Finally, solve for x X= -10 Now return to the equations in the problem statement, Substitute for x in either equation to solve for y. Since the second equation is already solved for y it will be easier to use. Substitute -10 for x in the second equation and simply Y= -6 Solve by the SUBSTITUTION Method 3x-9y= -6 7x+74=y 3x-9(7x+74)=-6 3x-63x- 666= -6 -60x= 660 X= -11 7(-11)+74= Y -77+74=Y Y= -3 The solution of the system is (-11,-3) Solve by the SUBSTITUTION Method 9x-2y= -80 8x+75=y
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9x-2(8x+75)= -80 9x-16x-150= -80 -7x=70 X= -10 8(-10)+75=y -80+75=Y -5=y The solution to the system is (-10,-5) Solve by the SUBSTITUTION method 5m+n=4 m-9n=10 **If the coefficient of a variable is 1 or -1, then it is easier to solve for that variable**
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This note was uploaded on 08/13/2011 for the course MAT 116 taught by Professor Universityofphoenix during the Spring '09 term at University of Phoenix.

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Week 7 notes - To solve a system of two equations in two...

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