Question

СРОЧНО! нужно решить эти две систему уравнений с помощью дискриминанта
$1)x + 3y = 7 \\ {x}^{2} - y = 9 \\ \\ 2)x - y = 1 \\ {x}^{2} - {y}^{2} = 9$
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Answer 1

1)

$\left \{ {{x+3y=7} \atop {x^2-y^2=9}} \right. =>\left \{ {{x=7-3y} \atop {x^2-y^2=9}} \right. \\\\(7-3y)^2-y^2=9\\49-42y+9y^2-y^2=9\\8y^2-42y+40=0 \ (:2)\\4y^2-21y+20=0\\D=441-320=121=11^2\\y_1=(21-11)/8=10/8=5/4\\y_2=(21+11)/8=4\\\\\left \{ {{x=7-3*\frac{5}{4} } \atop {x=7-3*4}} \right. =>\left \{ {{x_1=\frac{13}{4} } \atop {x_2=-5}} \right.$

ОТВЕТ: $x_1=\frac{13}{4} \\x_2=-5\\y_1=\frac{5}{4} \\y_2=4$

2)

$\left \{ {{x-y=1} \atop {x^2-y^2=9}} \right. =>\left \{ {{x=1+y} \atop {x^2-y^2=9}} \right. \\\\(1+y)^2-y^2=9\\1+2y+y^2-y^2=9\\2y=8\\y=4\\\\x=1+y=1+4=5\\x=5$

ОТВЕТ: $x=5\\y=4$