ExpandStr\( \mathrm { 3 \cdot x - 2 \cdot y = 7 } \)ProcessLogAdd \( \mathrm { 2 \cdot y } \) to both sidesStr\( \mathrm { 3 \cdot x - 2 \cdot y + 2 \cdot y = 7 + 2 \cdot y } \)ProcessLog\( \mathrm { - 2 \cdot y + 2 \cdot y = 0 } \)Str\( \mathrm { 3 \cdot x + 0 = 7 + 2 \cdot y } \)ProcessLogMultiply both sides with \( \mathrm { \displaystyle\frac{1}{3} } \)Str\( \mathrm { \displaystyle\frac{3}{3} \cdot x = \left(7 + 2 \cdot y\right) \cdot \displaystyle\frac{1}{3} } \)StrProcessLog\( \mathrm { \displaystyle\frac{3}{3} \cdot x = \left(7 + 2 \cdot y\right) \cdot \displaystyle\frac{1}{3} } \) \( \mathrm { \Longrightarrow } \) \( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3} } \)Str\( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3} } \)\( \mathrm { 3 \cdot x - 2 \cdot y = 7 } \)\( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3} } \)Isolate \( \mathrm { x } \)Str\( \mathrm { 5 \cdot x + y = 19 } \)ProcessLogReplace \( \mathrm { x } \) with \( \mathrm { \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3} } \)Str\( \mathrm { 5 \cdot \left(\displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3}\right) + y = 19 } \)ExpandStr\( \mathrm { 5 \cdot \left(\displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3}\right) + y } \)ProcessLogRewrite \( \mathrm { 5 \cdot \left(\displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3}\right) + y } \) with using the common denominator \( \mathrm { 3 } \) : \n \( \mathrm { \displaystyle\frac{35 + 10 \cdot y + 3 \cdot y}{3} } \)Str\( \mathrm { \displaystyle\frac{35 + 10 \cdot y + 3 \cdot y}{3} } \)ProcessLog\( \mathrm { 10 \cdot y + 3 \cdot y = 13 \cdot y } \)Str\( \mathrm { \displaystyle\frac{35 + 13 \cdot y}{3} = 19 } \)StrStrProcessLogUse the distributive property of multiplication: \n \( \mathrm { a \cdot ( b + c ) = a \cdot b + a \cdot c } \) \n \( \mathrm { \displaystyle\frac{35 + 13 \cdot y}{3} = \displaystyle\frac{35 + 13 \cdot y}{3} } \)StrProcessLogMultiply both sides with \( \mathrm { 3 } \)Str\( \mathrm { \displaystyle\frac{3}{3} \cdot \left(35 + 13 \cdot y\right) = 19 \cdot 3 } \)ProcessLogSimplify the numerator and denominator: \n \( \mathrm { \displaystyle\frac{3}{3} \cdot \left(35 + 13 \cdot y\right) = 35 + 13 \cdot y } \)ProcessLog\( \mathrm { 19 \cdot 3 = 57 } \)Str\( \mathrm { 35 + 13 \cdot y = 57 } \)ProcessLogAdd \( \mathrm { -35 } \) to both sidesStr\( \mathrm { 35 + 13 \cdot y - 35 = 57 - 35 } \)ProcessLog\( \mathrm { 35 - 35 = 0 } \)Str\( \mathrm { 0 + 13 \cdot y = 57 - 35 } \)ProcessLog\( \mathrm { 57 - 35 = 22 } \)Str\( \mathrm { 0 + 13 \cdot y = 22 } \)ProcessLogMultiply both sides with \( \mathrm { \displaystyle\frac{1}{13} } \)Str\( \mathrm { \displaystyle\frac{13}{13} \cdot y = 22 \cdot \displaystyle\frac{1}{13} } \)StrProcessLog\( \mathrm { \displaystyle\frac{13}{13} \cdot y = 22 \cdot \displaystyle\frac{1}{13} } \) \( \mathrm { \Longrightarrow } \) \( \mathrm { y = \displaystyle\frac{22}{13} } \)Str\( \mathrm { y = \displaystyle\frac{22}{13} } \)\( \mathrm { y = \displaystyle\frac{22}{13} } \)Isolate \( \mathrm { y } \)Str\( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot y}{3} } \)ProcessLogReplace \( \mathrm { y } \) with \( \mathrm { \displaystyle\frac{22}{13} } \)Str\( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot 22}{3 \cdot 13} } \)ExpandProcessLog\( \mathrm { 3 \cdot 13 = 39 } \)Str\( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{2 \cdot 22}{39} } \)ProcessLog\( \mathrm { 2 \cdot 22 = 44 } \)Str\( \mathrm { x = \displaystyle\frac{7}{3} + \displaystyle\frac{44}{39} } \)ProcessLog\( \mathrm { \displaystyle\frac{7}{3} + \displaystyle\frac{44}{39} = \displaystyle\frac{45}{13} } \)Str\( \mathrm { x = \displaystyle\frac{45}{13} } \)\( \mathrm { x = \displaystyle\frac{45}{13} } \)Simplify

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Solution: Solve the system: 3x - 2y equals 7 and 5x + y equals 19

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