Math Homewrk help: SUBSTITUTION?

Question

HELPPPP

A. x+2y=6
B. 3x-y=11

Answer 1

Solve equation A for x:
x = 6 - 2y

Substitute the result in for x in equation B:
3(6 - 2y) - y = 11

Distribute the 3:
18 - 6y -y = 11

Combine like terms:
-7y = -7

Divide the -7 through both sides of the equation:
y = 1

Substitute the y-value into equation A:
x + 2(1) = 6

And solve:
x + 2 = 6
x = 4

x = 4 and y = 1

Answer 2

Substitution is when you substitute a value for one of the variables in your problem.
Here you have the simultaneous equation above. You could substitute for x or y in this case. If you substituted for x, you'd have x=-2y+6, because you add -2y to both sides of the equation, eliminating the 2y on the left side, and getting -2y on the right side. Therefore, the left side only has x left, so your now have a working value for x in this equation.
Then, you substitute -2y+6 in for x in either equation. Let's do it in equation B. You'd have 3(-2y+6)-y=11. Then, using the distributive property, you'd have -6y+18-y=11. Then you'd add the two x terms on the left side, then getting -7y+18=11. Then you add -18 to both sides of the equation, getting -7y=-7. You divide -7 on both sides to get y alone. Since -7/-7=1, y=1.
Then, to find x, we could plug in 1 for y in equation A. You'd then have x+2=6. Then, subtracting 2 from both sides, you'd have x=4.
To check the values, just plug in the values for x and y into the original equations. If you check these values, they work. So, therefore, your values are x=4 and y=1, or ordered pair (4,1).
Another approach would be to substitute for y. You'd get the same answer this way too, though.
Well, there you go. I hope I helped you. :)

Answer 3

X + 2Y = 6
3X - Y = 11 [=> MULTIPLY *2]

X + 2Y = 6
6X -2Y = 22 [ADD THE 2 EQ.]
___________
7X +2Y -2Y = 28

7X = 28
X = 4

SUBST X IN {X + 2Y = 6 }
4 + 2Y = 6
2Y = 6 - 4 = 2
Y = 2/2
Y = 1