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Solve the systems using substitution. please show work just dont understand how

 3x + 2y = 6

x + 2y = -6

. 5x - 4y = 9

x - 2y = -3

 x + 3y = 5

4x + 5y = 13

x + 3y = 8

2x - y = 9

Verified Answer :

texaschic101

first, we need to pick an equation and isolate a variable
x + 2y = -6
x = -2y - 6
so we sub in -2y - 6 in for x in the other equation
3x + 2y = 6
3(-2y - 6) + 2y = 6...distribute through the parenthesis
-6y - 18 + 2y = 6
-6y + 2y = 6 + 18
-4y = 24
y = 24/-4
y = - 6
now we sub -6 in for y in either of the original equations..and solve for x
3x + 2y = 6
3x + 2(-6) = 6
3x -12 = 6
3x = 6 + 12
3x = 18
x = 18/3
x = 6

check...
x + 2y = -6
6 + 2(-6) = -6
6 - 12 = -6
-6 = -6 (correct)
so the solution is : (6,-6)

so basically, u first isolate a variable....it does not matter which one. And then u sub that back into the other equation and find the other variable. Once that is found, sub that into either of the equations and find the other variable. Also, you should check ur solutions by subbing the values u got into either original equation to see if it is true.

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