7.) {y+2x=11, x+y=5 ---- -- -- (8.)x-10y-2 , x-6y=6 ---- -- -- (9.) 8x=y , 2x+y=5?

Question

use substitution to solve each system of equations. check the solution?
please help summer practice

Answer 1

Hi,

7.) y+2x=11
x+y=5

Solving the first equation for y, y = 11 - 2x. Substituting that into the second equation, it becomes:

x+y=5
x+11-2x=5 Simplify this:
-x+11=5
-x =-6
x=6
If x = 6, then x+y=5 becomes 6+y=5, so y = -1

FIRST ANSWER: (6,-1)

8.) x-10y=2
x-6y=6

Solving the first equation for x, x = 10y+2. Substituting that into the second equation, it becomes:

x-6y=6
10y+2-6y = 6
4y+2 = 6
4y = 4
y = 1

If y = 1 is substituted into x-6y=6, it becomes: x -6(1) = 6 or
x - 6 = 6, so x = 12. The answer is (12,1). <== answer

9.) 8x=y
2x+y=5

Since y = 8x, 8x can be substituted into the second equation for y to make it:

2x+y=5
2x+8x=5
10x=5
x=½

If we substitute that back into y = 8x, then y = 8(½) or y = 4.

The answer is (½,4).



I hope that helps!! :-)

Answer 2

Question 7
y = 11 - 2x
x + (11 - 2x) = 5
- x + 11 = 5
- x = - 6
x = 6
y = - 1

Question 8 (guessing x - 10y = 2?)
x = 6 + 6y
6 + 6y - 10y = 2
-4y = - 4
y = 1
x = 12

Question 9
2x + 8x = 5
10x = 5
x = 0.5
y = 4

Answer 3

Okay, basically you isolate one variable in each problem and substitute it to find the answer.
For example, for number 7, you can subtract y from both sides in the second equation to get x=5-y. Now that you know what x is, you can substitute it in the first equation to get y+2(5-y)=11, which, after all the distributing and subtracting, gets you y=-1. Now, you can use that in the second equation, substitute y for -1 to get x-1=5, and so x=6.
Now you just apply that principle to the next two problems. =D
Hope that helped...