My teacher didnt explain it enough to know how to do the steps of the assignment but its not homework its assignment that i need to know how to do it like in each questions thanks !!!!!
12. 5x - 2y = -15
3x + 3y = 12
14. 2x - 3y = 2
5x + 4y = 28
16. -4x + 2y = 0
10x + 3y = 8
please show work as in each step of each question thank you!
12. 5x - 2y = -15
3x + 3y = 12
14. 2x - 3y = 2
5x + 4y = 28
16. -4x + 2y = 0
10x + 3y = 8
please show work as in each step of each question thank you!
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You "eliminate" one variable by adding together equations that are constructed from the initial ones.
Sometimes you are lucky and you simply add or subtract as is, but most of the time, you have to change at least one.
Remember that if you have
a = b
then you can multiply both sides by any number (same number on all terms) and the equation remains true
-7a = -7b
---
Question 12
If
5x - 2y = -15
then, we multiply everywhere by 3 to get
15x - 6y = -45
If
3x + 3y = 12
we multiply everywhere by 2 to get
6x + 6y = 24
Add together the two resulting equations (left with left, right with right) to get:
15x - 6y + 6x + 6y = -45 + 24
this leaves you with
21x = -21
The "y" has canceled out (you have eliminated it - hence the name of the method) and you are left with a much simpler equation to solve.
Once you have found the value for x, you can go back to any of the initial equations and use that value, in order to find y.
You can do it in any order you want (you can eliminate x first, to find y, if you think that is easier); you can use any factor you want (as long as it works), even fractions!
Question 16:
-4x + 2y = 0
multiply everywhere by 2.5 (two and a half)
4 * 2.5 = 10 and 2 * 2.5 = 5 and, of course, 0 * 2.5 = 0
-10x + 5y = 0
10x + 3y = 8
add together (the "x" cancels out)
8y = 8
y = 1
go back to the second one
10x + 3y = 8
10x + 3(1) = 8
10x + 3 = 8
10x = 5
x = 0.5 (= one half)
Sometimes you are lucky and you simply add or subtract as is, but most of the time, you have to change at least one.
Remember that if you have
a = b
then you can multiply both sides by any number (same number on all terms) and the equation remains true
-7a = -7b
---
Question 12
If
5x - 2y = -15
then, we multiply everywhere by 3 to get
15x - 6y = -45
If
3x + 3y = 12
we multiply everywhere by 2 to get
6x + 6y = 24
Add together the two resulting equations (left with left, right with right) to get:
15x - 6y + 6x + 6y = -45 + 24
this leaves you with
21x = -21
The "y" has canceled out (you have eliminated it - hence the name of the method) and you are left with a much simpler equation to solve.
Once you have found the value for x, you can go back to any of the initial equations and use that value, in order to find y.
You can do it in any order you want (you can eliminate x first, to find y, if you think that is easier); you can use any factor you want (as long as it works), even fractions!
Question 16:
-4x + 2y = 0
multiply everywhere by 2.5 (two and a half)
4 * 2.5 = 10 and 2 * 2.5 = 5 and, of course, 0 * 2.5 = 0
-10x + 5y = 0
10x + 3y = 8
add together (the "x" cancels out)
8y = 8
y = 1
go back to the second one
10x + 3y = 8
10x + 3(1) = 8
10x + 3 = 8
10x = 5
x = 0.5 (= one half)