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Solve the following linear equations using the Elimination method and The Substitution method
1) X + 3 Y = 2
2X + 5 Y = 3
2) 3X + 4 Y = 12
6X + 2 Y = 6
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First system is good to apply the Substitution method.
X + 3Y = 2 (1)
2X + 5Y = 3 (2)
From equation (1), express X = -3Y + 2. Then substitute it into equation (2), replacing X there.
You will get then
2*(-3Y + 2) + 5Y = 3 (3)
It is equation for one single unknown Y. Simplify it step by step and find Y
-6Y + 4 + 5Y = 3
-Y = 3 - 4
-Y = -1
Y = 1.
Now substitute the found value Y = 1 into equation (1) to find X.
X + 3*1 = 2,
or
X + 3 = 2,
X = 2 - 3 = -1.
ANSWER. The solution is X= -1, Y = 1.
Check it on your own that the found values SATISFY the given equations.
I did this check MENTALLY for myself.
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