If 3 x + 2 y = 12 and 2 x + 3 y = 13, find the value of x + y.

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{"type":"doc","content":[{"content":[{"text":"Step 1:","type":"text","marks":[{"type":"bold"}]},{"text":" Write the system of linear equations:","type":"text"}],"type":"paragraph"},{"attrs":{"start":1},"content":[{"type":"list_item","content":[{"content":[{"type":"math_inline","attrs":{"latex":"3x + 2y = 12"}}],"type":"paragraph"}]},{"content":[{"content":[{"attrs":{"latex":"2x + 3y = 13"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"}],"type":"ordered_list"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2:","type":"text"},{"text":" Add the two equations together:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"(3x + 2y) + (2x + 3y) = 12 + 13 \implies 5x + 5y = 25"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" Factor out ","type":"text"},{"attrs":{"latex":"5"},"type":"math_inline"},{"text":" on the left side:","type":"text"}]},{"attrs":{"latex":"5(x + y) = 25"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"text":" Divide both sides by ","type":"text"},{"attrs":{"latex":"5"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"x + y = \frac{25}{5} = 5"},"type":"math_block"},{"content":[{"text":"So the value of ","type":"text"},{"attrs":{"latex":"x + y"},"type":"math_inline"},{"type":"text","text":" is "},{"attrs":{"latex":"5"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"}]}

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