Can someone show me step by step how to do this problem to have an example to go by so I will be able to do my other problems. Thanks
Solve by substitution
4x-12y=5
-x+3y=-1
I know that you have solve one of the equations. I have picked the second one so it would be y= -1/3+1/3x right??
Then I substitute 4x-12(-1/3+1/3x)=5.
Now I have no clue what to do from there. Please help.
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.If that right?
In the bottom, rearrange to read
x= 3y+1
Now put that value for x in the top equation...
4x-12y=5
4( 3y+1)-12y=5
then solve for y.
when you get y, go back and put it in
x= 3y+1 to get x.
I suggest you show your number as
y=[(x-1)/3
Then 4x -12[(x-1)/3] = 5
Then 4x -4(x-1) = 5
etc. I'm sure you can handle it from here.
To solve the system of equations using substitution, you correctly solved the second equation for y as y = (-1/3) + (1/3)x.
Now, substitute this value of y into the first equation:
4x - 12*(-1/3 + 1/3x) = 5
Next, simplify the equation:
4x + 4/3 - 4/3x = 5
Combining like terms, we get:
4x - 4/3x + 4/3 = 5
To make it easier to work with, let's clear the denominators by multiplying all the terms by 3:
12x - 4x + 4 = 15
Simplify further:
8x + 4 = 15
Subtract 4 from both sides:
8x = 11
Divide both sides by 8:
x = 11/8
Now that we have the value of x, we can substitute it back into one of the initial equations to solve for y.
Using the second equation:
-x + 3y = -1
Replace x with 11/8:
-(11/8) + 3y = -1
Multiply through by 8 to clear the fraction:
-11 + 24y = -8
Add 11 to both sides:
24y = 3
Divide by 24:
y = 3/24 = 1/8
So the solution to the system of equations is x = 11/8 and y = 1/8.
Note: In this specific case, I made some calculations to show you the step-by-step process. However, you can speed up the overall process by multiplying the second equation by 4 to eliminate the 4x term, and then substituting the resulting equation into the first equation.