Need help with solving with substitution and elimination. Tell whether the system has one solution, infinitely many solutions, or no solution.
Solve using substitution:
13. –x + y = -13
3x – y = 19

15. 1/3y = 7/3x + 5/3
x – 3y = 5

17. 3x + y = -13
-2x +5y = -54

Solve using elimination: Tell whether the system has one solution, infinitely many solutions, or no solution.
19. x + 2y = 23
5x + 10y = 55

21. 5x + 4y = -83
3x - 3y = -12

23. 4x + y = 21
-2x + 6y = 9

Even if you can help by explaining it in simplest terms, that would be helpful.

Question

Need help with solving with substitution and elimination.  Tell whether the system has one solution, infinitely many solutions, or no solution.
Solve using substitution:
13.  –x + y = -13
     3x – y = 19

15.  1/3y = 7/3x + 5/3
     x – 3y = 5

17.  3x + y = -13
     -2x +5y = -54

Solve using elimination: Tell whether the system has one solution, infinitely many solutions, or no solution.
19.  x + 2y = 23
     5x + 10y = 55

21.  5x + 4y = -83
     3x - 3y = -12

23.  4x + y = 21
     -2x + 6y = 9

Even if you can help by explaining it in simplest terms, that would be helpful.

solomonzelman · Answer

13.     add the second equation to the first.  
          solve for y, and plug in then for x.
         SHOW YOUR STEPS HERE!    ( we are helping not giving answers on this website )

lovelyharmonics · Answer

13: y= x-13
now plug ^ equation into 3x-y=19

lovelyharmonics · Answer

as in, since y is equal to x-13 youre going to take x-13 and plug it into the other equation to replace y...
so 3x- (put it here) =19

texaschic101 · Answer

SUBSTITUTION :
13. -x + y = -13
      y = x - 13
now sub x - 13 in for y in the other equation
3x - y = 19
3x - (x - 13) = 19 -- distribute through the parenthesis
3x - x + 13 = 19 -- subtract 13 from both sides
3x - x = 19 - 13 -- combine like terms
2x = 6 -- divide both sides by 2
x = 3
now sub 3 in for x in either equation to find y
y = x - 13
y = 3 - 13
y = -10
check your answers...
-x + y = -13
-3 + (-10) = -13
-3 - 10 = -13
-13 = -13 (correct)
SOLUTION : x = 3 and y = -10 (ONE SOLUTION)
============================
ELIMINATION :
19. x + 2y = 23
     5x + 10y = 55 (this can be reduced to x + 2y = 11)
now we have :
x + 2y = 23
x + 2y = 11
Same slope, different y intercepts, ...that means the lines are parallel and do not intersect, therefore, there is NO SOLUTION.

However, if you want to see it worked out...
x + 2y = 23 --->(-5)
5x + 10y = 55
---------------
-5x - 10y = - 115 (result of multiplying by -5)
5x + 10y = 55
---------------add
0 + 0 = - 60
0 = 60 (incorrect)
They will not intersect, NO SOLUTION
============================
There are two of the problems, one by substitution, and the other by elimination.

Any questions, just ask :)

anonymous · Answer

Thank you so much for the help.  I understand it better now!