8-2a Simultaneous Solutions

More info here , notes here, and on pages 362-364 in book


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Steps for substitution:

1) Isolate a variable (for instance x=... or y=...)

2) Substitute the isolated variable in for itself in the other equation.

3) Solve the new equation which now has only one variable

4) Use the value of the variable to plug in to one of the original equations to find the missing side of the coordinate pair.

Example:

For the equations, y+2=2x and 2y+3x=10
What are the coordinates of the simultaneous solution?

ISOLATE: Easiest to isolate y in first equation by adding 2 to both sides: y=2x-2

SUBSTITUTE: 2(2x-2)+3x=10

SOLVE: 4x - 4 + 3x = 10 ==> eventually gets you 7x = 14 which means x=2

PLUG IN: Pick either of the two equations to plug in x=2. You should get the same answer for y.

y + 2 = 2(2)

gives

y = 2

whereas

2y+3(2)=10

also gives

y=2

So the solution is (2,2)