Richard has three times as many crayons as Jordan. Together they have 60 crayons. How many crayons does
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Question: Which system has the same solution as the teacher's system?
Systems of equations that have the same solution are called equivalent systems.We are given with a system of two equations, we can make an equivalent system by substituting one equation by the sum of the two equations.
Given System:
<span>
8x-16y=14</span>→eq.1
−x+5y=−3→eq.2<span>
Teacher's Solution:
From eq.2
x = 5y + 3
Substituting the value of x in eq.1
We get,
</span> 8(5y + 3) - 16y = 14
40y + 24 - 16y = 14
24y + 24 = 14
24y = 14-24
24y = -10
y = -10/24
y = -5/12
Substituting y-value in eq.2,
−x+5(-5/12) = −3
-x -25/12 = -3
-x = -3 + 21/12
-x = 15/12
x = -5/4
<span>Fabiano:
</span> 3x−15y=<span>9
</span> 8x−16y=−<span>7
</span>Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x+7/16
Placing both equations equal to each other,
1/5x - 3/5= 1/2x+7/16
1/5x -1/2x = 7/16 +3/5
-3/5x = 83/80
x = -83×5/80×3
x = -415/240
x = -83/48
This doesnt matches the teachers solution so we will move to sonali.
<span>Sonali
</span> −x+5y=−<span>3
</span> −4x+8y=−7
Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x -7/8
Placing both equations equal to each other,
1/5x - 3/5 = 1/2x -7/8
1/5x -1/2x = -7/8 +3/5
-3/10x = -11/40
x = 110/120
x = 11/12
This doesn't match the teacher's solution either, so we will conclude that none of the solutions to the system of equation has the same answer as the teacher.
Systems of equations that have the same solution are called equivalent systems.We are given with a system of two equations, we can make an equivalent system by substituting one equation by the sum of the two equations.
Given System:
<span>
8x-16y=14</span>→eq.1
−x+5y=−3→eq.2<span>
Teacher's Solution:
From eq.2
x = 5y + 3
Substituting the value of x in eq.1
We get,
</span> 8(5y + 3) - 16y = 14
40y + 24 - 16y = 14
24y + 24 = 14
24y = 14-24
24y = -10
y = -10/24
y = -5/12
Substituting y-value in eq.2,
−x+5(-5/12) = −3
-x -25/12 = -3
-x = -3 + 21/12
-x = 15/12
x = -5/4
<span>Fabiano:
</span> 3x−15y=<span>9
</span> 8x−16y=−<span>7
</span>Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x+7/16
Placing both equations equal to each other,
1/5x - 3/5= 1/2x+7/16
1/5x -1/2x = 7/16 +3/5
-3/5x = 83/80
x = -83×5/80×3
x = -415/240
x = -83/48
This doesnt matches the teachers solution so we will move to sonali.
<span>Sonali
</span> −x+5y=−<span>3
</span> −4x+8y=−7
Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x -7/8
Placing both equations equal to each other,
1/5x - 3/5 = 1/2x -7/8
1/5x -1/2x = -7/8 +3/5
-3/10x = -11/40
x = 110/120
x = 11/12
This doesn't match the teacher's solution either, so we will conclude that none of the solutions to the system of equation has the same answer as the teacher.