SOLUTION: Which ordered pair is a solution of the system of equations? (x,y) y=3x+1 y=5x-3 A. (2,3) B. (0,1) C. (1,2) D. (2,7)

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Which ordered pair is a solution of the system of equations? (x,y) y=3x+1 y=5x-3 A. (2,3) B. (0,1) C. (1,2) D. (2,7)      Log On


   

Question 151611: Which ordered pair is a solution of the system of equations? (x,y)
y=3x+1 y=5x-3
A. (2,3) B. (0,1) C. (1,2) D. (2,7)
Found 3 solutions by jojo14344, mangopeeler07, jim_thompson5910:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Equating the 2 eqns;
3x%2B1=5x-3
5x-3x=1%2B3
cross%282%29x%2Fcross%282%29=cross%284%292%2Fcross%282%29
x=2
for y,
y=3*2+1, ------> y=7
(2,7)
Answer: D
Thank you,
Jojo

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
plug in the solutions for A, B, C, and D.

y=3x+1
y=5x-3

A. (2,3)

3=3(2)+1
3=5(2)-3
WRONG

Answer: not A
-------------------------------------------------------------------------
B. (0,1)

1=3(0)+1
1=5(0)-3
WRONG

Answer: not A or B
--------------------------------------------------------------------------
C. (1,2)

2=3(1)+1
2=5(1)-3
WRONG

Answer: not A, B, or C
---------------------------------------------------------------------------
At this point, we know the answer is D, but let's do it anyway.
D. (2,7)

7=3(2)+1
7=5(2)-3
RIGHT

Answer: D

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the answer, let's check all of the possible answers (note: an alternative is to solve the system)

A)


Let's see if (2,3) is a solution.


y=3x%2B1 Start with the first equation.


%283%29=3%2A%282%29%2B1 Plug in x=2 and y=3.


3=3%2A%282%29%2B1 Evaluate and simplify the left side.


3=7 Evaluate and simplify the right side.


Since the equation is not true, this means that (2,3) is not a solution.


Let's see if (2,3) is a solution.


y=5x-3 Start with the second equation.


%283%29=5%2A%282%29-3 Plug in x=2 and y=3.


3=5%2A%282%29-3 Evaluate and simplify the left side.


3=7 Evaluate and simplify the right side.


Since the equation is not true, this means that (2,3) is not a solution.


Since at least one of the equations of the system is false, this means that (2,3) is not a solution. Remember, a solution must satisfy all of the equations in the system.




B)



Let's see if (0,1) is a solution.


y=3x%2B1 Start with the first equation.


%281%29=3%2A%280%29%2B1 Plug in x=0 and y=1.


1=3%2A%280%29%2B1 Evaluate and simplify the left side.


1=1 Evaluate and simplify the right side.


Since the equation is true, this means that (0,1) is a solution.


Let's see if (0,1) is are a solution.


y=5x-3 Start with the second equation.


%281%29=5%2A%280%29-3 Plug in x=0 and y=1.


1=5%2A%280%29-3 Evaluate and simplify the left side.


1=-3 Evaluate and simplify the right side.


Since the equation is not true, this means that (0,1) is not a solution.


Since at least one of the equations of the system is false, this means that (0,1) is not a solution. Remember, a solution must satisfy all of the equations in the system.




C)


Let's see if (1,2) is a solution.


y=3x%2B1 Start with the first equation.


%282%29=3%2A%281%29%2B1 Plug in x=1 and y=2.


2=3%2A%281%29%2B1 Evaluate and simplify the left side.


2=4 Evaluate and simplify the right side.


Since the equation is not true, this means that (1,2) is not a solution.


Let's see if (1,2) is a solution.


y=5x-3 Start with the second equation.


%282%29=5%2A%281%29-3 Plug in x=1 and y=2.


2=5%2A%281%29-3 Evaluate and simplify the left side.


2=2 Evaluate and simplify the right side.


Since the equation is true, this means that (1,2) is a solution.


Since at least one of the equations of the system is false, this means that (1,2) is not a solution. Remember, a solution must satisfy all of the equations in the system.




D)




Let's see if (2,7) is a solution.


y=3x%2B1 Start with the first equation.


%287%29=3%2A%282%29%2B1 Plug in x=2 and y=7.


7=3%2A%282%29%2B1 Evaluate and simplify the left side.


7=7 Evaluate and simplify the right side.


Since the equation is true, this means that (2,7) is a solution.


Let's see if (2,7) is a solution.


y=5x-3 Start with the second equation.


%287%29=5%2A%282%29-3 Plug in x=2 and y=7.


7=5%2A%282%29-3 Evaluate and simplify the left side.


7=7 Evaluate and simplify the right side.


Since the equation is true, this means that (2,7) is a solution.


Since all of the equations of the system are true, this means that (2,7) is a solution



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Answer:

So the solution is D) (2,7)