Solve the following equations: 7x-4y=-10 and 4y=x-2.
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We have to solve the simultaneous equations
7x-4y=-10 ...(1)
4y=x-2...(2)
add (2) and (1)
=> 7x - 4y + 4y = -10 + x - 2
=> 7x = -12 + x
=> 6x = -12
=> x = -2
Substitute this in (2)
4y=x-2
=> 4y = -2 - 2
=> 4y = -4
=> y = -1
Therefore we get x = -2 and y = -1.
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7x-4y= -10. Or -4y = -7x-10...(2)....(1)
4y =x-2, or 4y = x-2 ...(2).
(1)+(2) eliminates y: -4y+4y = -7x-10+x-2.
=> 0 = -7x+x-10-2.
=> 0 = -6x-12.
=> 6x= -12. Or x = 12/-6 = -2.
Put x= -2 in 4y= x-2 . 4y = -2-2 = -4, or y = -4/4 = -1.
Therefore x= -2 and y = -1.
So x= 1 and y = -2.
To perform elimination method we need to have 2 like variables that have opposite sign.
To see more clear how to act, we'll need to write both equations in the same manner: we'll isolate to the left side the variables and we'll move the numbers alone to the right side.
The first equation needs no changes but the second will turn into:
4y - x = -2
We'll re-arrange the terms:
-x + 4y = -2
Now, the system will become:
7x - 4y = -10 (1)
-x + 4y = -2 (2)
We can remark that we can eliminate the variable y, since in both equations there are terms 4y and -4y.
We'll add (1)+(2) to eliminate y;
7x - 4y - x + 4y = -10 - 2
We'll combine and eliminate like terms:
6x = -12
We'll divide by 6:
x = -2
Now, we'll substitute x in the second equation:
-(-2) + 4y = -2
2 + 4y = -2
We'll subtract 2 to isolate y to the left side:
4y = -4
y = -1
The solution of the system solved using elimination method is: (-2 ; -1).
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