Answer:
19 substitution
20 elimination
21 elimination
22 elimination
Step-by-step explanation:
19.) x + y = 2
y = 2x - 1
Substitution, since the second equation is already solved for y
x + (2x-1) =2
Combine like terms
3x-1 =2
Add 1 to each side
3x-1+1= 2+1
3x=3
Divide by 3
x=1
Now we need y
x+y =2
1+y= 2
Subtract 1
y=1
(1,1)
20.) - x - 5y = 7
x + y = 1
I will used elimination since there is an x and a -x
- x - 5y = 7
x + y = 1
-------------------
-4y = 8
Divide by -4
-4y/-4 = 8/-4
y = -2
x+y =1
x-2=1
Add 2 to each side
x-2+2=1+2
x=3
(3,-2)
21.) 3x + y = 26
3x + 3y = 26
I will use elimination by multiplying the second equation by -1
3x + y = 26
-3x - 3y = -26
---------------------
-2y = 0
Divide by -2
-2y/-2 = 0/-2
y =0
Now we need to find x
3x + 0 = 26
Divid by 3
3x/3 = 26/3
x = 26/3
(26/3 ,0)
22.) 4x - 8y = 52
7x + 4y = 1
I will use elimination by multiplying the second equation by 2
2( 7x + 4y = 1 )
14x +8y =2
The add this to the first equation to eliminate y
4x - 8y = 52
14x +8y =2
--------------------
18x = 54
Divide by 18
18x/18 = 54/18
x=3
Now we need to find y
7x + 4y = 1
7(3) +4y = 1
21 +4y = 1
Subtract 21 from each side
21-21 +4y = 1-21
4y = -20
Divide by 4
4y/4 = -20/4
y=-5
(3,-5)
