document.write( "Question 128384: Tell whether the ordered pair is a solution of the linear system.\r
\n" ); document.write( "\n" ); document.write( "(-2,15);
\n" ); document.write( "y = -3x + 9
\n" ); document.write( "y = 5x + 25\r
\n" ); document.write( "\n" ); document.write( "Someone please help me with this equation,any help would be appreciated :) \n" ); document.write( "
Algebra.Com's Answer #93986 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
All these two problems involve is taking the x value of the given point and substituting
\n" ); document.write( "it in for x in the equation, then taking the y value of the given point and substituting
\n" ); document.write( "it for y in the equation, and finally seeing if the equation still balances. If it does, then
\n" ); document.write( "you can say the ordered pair of the point is a solution of the linear system.
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\n" ); document.write( "Let's do it. The given point (or ordered pair) has an x value of -2 and a y value of +15.
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\n" ); document.write( "Go to the first equation and substitute -2 for x and + 15 for y. This is done as follows:
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\n" ); document.write( "y = -3x + 9
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\n" ); document.write( "Substitute -2 for x and +15 for y and the equation becomes:
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\n" ); document.write( "+15 = -3(-2) + 9
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\n" ); document.write( "Multiply the -3 times the -2 to get +6 and this makes the equation become:
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\n" ); document.write( "+15 = +6 + 9
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\n" ); document.write( "The sum on the right side is +15 and this makes the equation:
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\n" ); document.write( "+15 = +15
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\n" ); document.write( "Since the equation is balanced (both sides are equal) this tells us that that the ordered
\n" ); document.write( "pair (-2, 15) is a solution of the first equation.
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\n" ); document.write( "Now let's go to the second equation you were given:
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\n" ); document.write( "y = 5x + 25
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\n" ); document.write( "Substitute -2 for x and +15 for y and the equation becomes:
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\n" ); document.write( "+15 = 5(-2) + 25
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\n" ); document.write( "Multiply the 5 times the -2 on the right side to get -10 and the equation is then:
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\n" ); document.write( "+15 = -10 + 25
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\n" ); document.write( "The two numbers on the right side combine to give +15 and the equation is then:
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\n" ); document.write( "+15 = +15
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\n" ); document.write( "The equation balances again and this tells you that the ordered pair (-2, +15) is a solution
\n" ); document.write( "of the second equation too.
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\n" ); document.write( "Since the ordered pair is a solution of BOTH equations, then it is a solution of the linear set
\n" ); document.write( "that contains both equations.
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\n" ); document.write( "Another way you could have done the problem is to solve the pair of equation to see if the
\n" ); document.write( "solution of the pair is x = -2 and y = +15. You can do this by substitution or by variable
\n" ); document.write( "elimination, or by graphing the two equations and finding the ordered pair where the two
\n" ); document.write( "graphs intersect.
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\n" ); document.write( "Let's use substitution.
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\n" ); document.write( "Since the left sides of both equations are both y, the two left sides are equal. And since
\n" ); document.write( "the left sides are both equal, then the two right sides also must be equal in the common solution.
\n" ); document.write( "In effect we are substituting the value of y from one of the equations (the right side of
\n" ); document.write( "that equation) for y in the other equation.
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\n" ); document.write( "When we do that substitution we get:
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\n" ); document.write( "-3x + 9 = 5x + 25
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\n" ); document.write( "Get rid of the 5x on the right side by subtracting 5x from both sides to get:
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\n" ); document.write( "-8x + 9 = 25
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\n" ); document.write( "Next get rid of the +9 by subtracting +9 from both sides to reduce the equation to:
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\n" ); document.write( "-8x = 16
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\n" ); document.write( "Solve for x by dividing both sides of this equation by -8 and you have:
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\n" ); document.write( "x = 16/-8 = -2
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\n" ); document.write( "This tells you that the solution of the set of equations has -2 as its value for x. Knowing
\n" ); document.write( "that x = -2 you can now return to either of the two original equations, substitute -2
\n" ); document.write( "for x in that equation, and find the value of y. Let's return to the original equation:
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\n" ); document.write( "y = 5x + 25
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\n" ); document.write( "Substitute -2 for x and the equation becomes:
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\n" ); document.write( "y = 5(-2) + 25 = -10 + 25 = +15
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\n" ); document.write( "This tells you the common solution to the two equations is x = -2 and y = +15 which is in
\n" ); document.write( "ordered pair form (-2, 15) and this is the point you were asked about. So the ordered pair
\n" ); document.write( "(-2, 15) is a solution to the set of equations, just as we found by doing it the other way.
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\n" ); document.write( "Hope this helps you to understand what you were being asked to do and how you would do it.
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