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Simultaneous Equations with same coefficients

Updated: Sep 6, 2020


Simultaneous equations are two equations with more than one unknown. An example is

2x-2y=6

5x+2y=36

In both equations x and y would be the same so you can now figure it out. First, you must take two unknown values with the same coeficcient. For example in equation a the coeficcient of y is 2 same as in equation b. The coefficcient of x in equation a is also 2. The two values with the same coeficcient are y. Now we need to add or subtract the equations so that letter y is not present. So we have 2y and – 2y if we subtract them it would be 2 - -2y which would equal 4y so we need to add them which would give us 0y which is 0. But we don’t only add one value we have to add the whole equation so it would be 2x-2y=6 + 5x+2y=36 We already know that y is 0 so therefore we do 5x+2x=7x and 36+6=42. W3 are left with the answers which are 7x=42 so therefore x=6. Now, we can substitute x to find out y. We take a look at the first equation and substitute x in. We are left with 2(6)-2y=6 which is 12-2y=6 and so y is 3.

X=6

Y=3

Here is another equation that you can try to solve yourself.

2x-4y=8

4x-4y=4

Again, we find the two coeficcients that are the same. Here it is 4y and both of the values are -4y (don’t look at the sign 4 and -4 are the same coeficcient) if we add -4y+-4y we get -8y so we have to subtract both equations as -4y - -4y=0 and we are trying to eliminate y. WE now swubrtact the other values to get 2x-4x=-2x -4y - -4y=0 8-4=4. As y is zero we are left with -2x=4 so x = -2. Now we substitute x into the first (or second) equation. We receive 4(-2)-4y=4 which is -8-4y=4 here we can divide both sides by 4 to get -2-y=1 and therefore y=-3

X=-2

Y=-3.

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