x+2y=3
5x+4y=8
I isolated x+2y=3 to make: x=3-2y
then i began to sub in equation one with equation two:
5x+4y(3-2y)=8
5x+12-8y=8
after that i began to try to solve the equation but my answers were not correct. any help would be greatly appreciated!
You are substituting for y instead of x
Besides that you were still keeping the y as well.
5(3-2y) + 4y = 8
15 - 10y + 4y = 8
-6y = -7
y = 7/6
then in x = 3-2y
x = 3-14/6 = 2/3
x = 2/3 , y = 7/6
i understand how you got the answer i just don't get why i don't put 5x+4y before the equation because i have been for all the other ones and i got those ones right..
for example this one:
6x+5y= 7
x-y= 3
i isolated the second equation into y=3+x
so: 6x+5y(3+x)=7
6x+15+5x=7
6x+5x-15+15=7+15
11/11= 22/11
x=2
then i subbed in the other equation..
6(2)+5y=7
12+5=7-12
5y/5= -5/5
y= -1
and i checked my answer and it was correct.
i just don't understand what i'm doing wrong for the equation.. because i keep thinking the full equation must go first not separate it.
Horizontal line through(5,0)
-2(2y+15)<-6y-14
It seems like you made a mistake while substituting the equations. Let's go through the correct process step by step:
1. Start with the given system of equations:
x + 2y = 3 ...(Equation 1)
5x + 4y = 8 ...(Equation 2)
2. Isolate x in Equation 1:
x = 3 - 2y
3. Substitute the value of x from Equation 1 into Equation 2:
5(3 - 2y) + 4y = 8
4. Distribute the 5 through the parentheses:
15 - 10y + 4y = 8
5. Simplify the equation:
-10y + 4y = 8 - 15
-6y = -7
6. Divide both sides of the equation by -6 to solve for y:
y = (-7) / (-6)
y = 7/6
7. Substitute the value of y back into Equation 1 to solve for x:
x + 2(7/6) = 3
8. Simplify the equation:
x + 14/6 = 3
x + 7/3 = 3
9. Subtract 7/3 from both sides of the equation:
x = 3 - 7/3
x = 9/3 - 7/3
x = 2/3
So, the solution to the system of equations is x = 2/3 and y = 7/6. Double-check your steps to see if you made any calculation error along the way.