2*2 Simultaneous Equations

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What are they?

1) We have 2 systems of equations.

1b) This means we're basically finding 2 solutions that fit both equations.

1c) Those 2 solutions will be x and y, which are 2 points, (The points of intersection)

Work it out

2) Use "substitution" to substitute equation 1 into 2. NOTE: We can do this because the value of equation is in slope form, & y = 1 / 1y = (xm + c)

3) When using substitution, one of the equations has to be in standard form, or y + x = c. This is important because it allows us to substitute in equation 1 (y = x+2) into equation 2 (1/4x + y = 0)

4) Since equation 2's y = 1. When we sub in (x+2) its just 1(x+2) Say equation 2 was 1/4x + 2y = 0, then you would go 2(x+2) and expand. So you have 1/4x + x + 2 = 0. Now since x is unknown and we only have knowledge of such values like 1/4x and x, when we add them, it's literally just 1 + 1/4. Which equals 5/4 or 1.25 (Keep in fraction)

5) We now have 5/4x + 2 = 0, but we want x by itself so we subtract 2 on both sides. so 5/4x = -2. Now remember to workout x, it has to equal 1, so times both sides of the equation so x will be equal to one, and the other side to balance the equation.

6) 5x = -8. So now get x to equal one by dividing both sides by 5. x = (-8/5)

7) So finally we have x, -8/5 and thats the result from substituting 1 into 2. But now we're gonna substitute x back into equation 1 to find the value of y.

8) So y = 1(-8/5) + 2.

To add them we need the same demoninator, lets chose 10.

so -16/10 + 20/10 = 4/10 or 2/5.

we're done! X = -8/5 and Y = 2/5