Solve each system using substitution. Tell whether the system has one solution, infinitely many solutions, or no solution.
13. -x + y = -13
3x - 1 = 19
15. 1/3y= 7/3 x + 5/3
x - 3y = 5
17. 3x + y = -13
-2x + 5y = -54
Oh yeah sorry. i didn't see it. for number one it was 3x-y=19
13. -x + y = -13
3x - 1 = 19
Is that a typo? No y in second equation? That sure makes it easy.
15.
y = (7 x + 5)
x - 3(7x+5) = 5
x - 21 x - 15 = 5
-20 x = 20
x = -1
y = -2
17.
y = (-3x - 13)
-2x + 5 (-3x-13) = -54
or
2x + 5 (3x+13) = 54
17 x + 65 = 54
17 x = - 11
x = -11/17
y = 33/17 -13 = 33/17 - 221/17 = -188/17
Oh thanks ! and for number one that's how the equations was written
13.
-x + y = -13
3x - y = 19
--------------- too easy to add them
2 x + 0 = 6
x = 3
y = -10
Thank you so much can you help me with couple more?
Do not do it the way I did it. Use substitution, but you should get the same answer.
You should be able to do them yourself now.
To solve a system of equations using substitution, follow these steps:
1. Select one equation from the system and isolate one variable in terms of the other variable.
2. Substitute the expression for the isolated variable into the other equation of the system.
3. Solve the resulting equation for the remaining variable.
4. Substitute the found value of the remaining variable back into one of the original equations to find the value of the previously isolated variable.
5. Check the solution by substituting the found values into both equations of the system.
Let's solve each system using substitution:
13. -x + y = -13
3x - 1 = 19
From the first equation, isolate y:
y = x - 13
Substitute this value into the second equation:
3x - 1 = 19
3x = 20
x = 20/3
Substitute the value of x back into the equation y = x - 13:
y = (20/3) - 13
y = -39/3
So the solution is x = 20/3, y = -39/3, which simplifies to x = 6.67, y = -13.
There is one unique solution for this system.
15. 1/3y = 7/3 x + 5/3
x - 3y = 5
From the first equation, isolate y:
y = (7/3)x + 5/3
Substitute this value into the second equation:
x - 3((7/3)x + 5/3) = 5
x - (7x + 15)/3 = 5
Multiply through by 3 to eliminate fractions:
3x - 7x - 15 = 15
-4x - 15 = 15
-4x = 30
x = -30/4
x = -7.5
Substitute the value of x back into the equation y = (7/3)x + 5/3:
y = (7/3)(-7.5) + 5/3
y = -17.5/3 + 5/3
y = -12.5/3
So the solution is x = -7.5, y = -12.5/3, which simplifies to x = -7.5, y = -4.17.
There is one unique solution for this system.
17. 3x + y = -13
-2x + 5y = -54
From the first equation, isolate y:
y = -3x - 13
Substitute this value into the second equation:
-2x + 5(-3x - 13) = -54
-2x -15x - 65 = -54
-17x - 65 = -54
-17x = -54 + 65
-17x = 11
x = 11/-17
x = -0.65
Substitute the value of x back into the equation y = -3x - 13:
y = -3(-0.65) - 13
y = 1.95 - 13
y = -11.05
So the solution is x = -0.65, y = -11.05.
There is one unique solution for this system.