You can put this solution on YOUR website! As your problem is written, you just need to follow 2 steps:
1) Solve the equation with only 1 variable
2) Plug that number into the other equation, and solve for the other variable.
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In your case: Step #1
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Step #2
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But, I'm going to assume you left out the "x" from equation 2. If correct, your question should read:
"I need to be shown the steps to solve a problem like {3x+2y=2 ; -2x+2y=16}"
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Step 1: "Stack" the equations on your paper, by writing 1 directly above the other (Notice that the x's and y's line up vertically)
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Step 2: Make each equation have either the same number of X's or Y's. In your case, you lucked out. Both start with 2y. So you need to remove them somehow. Either add or subtract. (2y+2y=4y), (2y-2y=0) - so we'll go with subtract.
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Step 3: Plug this answer back into one of the original formulas. Always go with the easier formula.
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In this case, neither is a good formula, so just pick the 1st.
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Hope this helps!