I am confused on how solve this substitution problem
4y+3=3y+x
2x+4y=18
If you can, show work please (:
I am pretty sure this goes like this
4y+3=3y+x (i)
2x+4y=18 (ii)
Rearrange (i) so that x=4y+3-3y
Take (ii) and sub x
it will become 2(4y+3-3y)+4y= 18
2(y+3)+4y =18
2y+6+4y=18
6y+6=18
6y=18-6
6y=12
y=12/6
y=2 (iii)
Now use what you found for y in (iii) and sub in the (ii or i to get x)
lets take (i) 4y+3=3y+x
from (iii) 4(2)+3=3(2)+x
11=6+x
x= 11-6
x=5
let me know if that's clear enough
Yes that is thank you so much (:
Sure, I can help you with that!
To solve the system of equations using substitution, we'll start by solving one of the equations for one variable and then substituting that expression into the other equation. Let's solve the first equation for x:
4y + 3 = 3y + x
To isolate x, we need to get rid of the y term on the right side. We can do this by subtracting 3y from both sides:
4y - 3y + 3 = x
Simplifying this gives us:
x = y + 3
Now, we can substitute this expression for x into the second equation:
2x + 4y = 18
Substituting x with y + 3:
2(y + 3) + 4y = 18
Simplifying this equation:
2y + 6 + 4y = 18
Combining like terms:
6y + 6 = 18
Next, we'll isolate the variable y by subtracting 6 from both sides:
6y = 18 - 6
Simplifying further:
6y = 12
Finally, we can solve for y by dividing both sides by 6:
y = 12/6
y = 2
Now that we know the value of y, we can substitute it back into either of the original equations to find x. Let's use the first equation:
4y + 3 = 3y + x
Substituting y with 2:
4(2) + 3 = 3(2) + x
Simplifying:
8 + 3 = 6 + x
Combining like terms:
11 = 6 + x
Subtracting 6 from both sides:
5 = x
So the solution to the system of equations is x = 5 and y = 2.