2x - 4y = 10
7x - 9y = 12
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Solve for x in the first equation. Add 4y to both sides.
2x = 10 + 4y
Divide both sides by 2.
x = 5 + 2y
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Plug in x into the second equation.
7(5 + 2y) - 9y = 12
Distribute 7 inside the parentheses.
35 + 14y - 9y = 12
Combine like terms.
35 + 5y = 12
Subtract 35 from both sides.
5y = -23
Divide both sides by 5.
y = -23/5
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Plug y into the first equation.
2x - 4(-23/5) = 10
Distribute -4 inside the parentheses.
2x + (92/5) = 10
Subtract 92/5 from both sides.
2x = -84/10 => 2x = -42/5
Divide both sides by 2.
x = -21/5
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[tex] \boxed {(-21/5, -23/5)} [/tex] is your answer.
