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GCD & LCMmedium
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The equation 21x+14y=721x + 14y = 721x+14y=7 has particular solution (x0,y0)=(1,−2)(x_0, y_0) = (1, -2)(x0​,y0​)=(1,−2). Verify: 21(1)+14(−2)=21−28=−721(1) + 14(-2) = 21 - 28 = -721(1)+14(−2)=21−28=−7... Let me use (x0,y0)=(3,−4)(x_0, y_0) = (3, -4)(x0​,y0​)=(3,−4): 21(3)+14(−4)=63−56=721(3) + 14(-4) = 63 - 56 = 721(3)+14(−4)=63−56=7 ✓. The general solution is x=3+2tx = 3 + 2tx=3+2t, y=−4−3ty = -4 - 3ty=−4−3t. Which is also a solution?