[tex]1) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{x + y = 4} \atop {x - y = 5}} \right. + \\ 2x = 9 \\ x = 4.5 \\ \\ x + y = 4 \\ 4.5 + y = 4 \\ y = 4 - 4.5 \\ y = - 0.5[/tex]
[tex]2) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{3x - 7y = 11} \atop {6x + 7y = 16}} \right. + \\ 9x = 27 \\ x = 3 \\ \\ 6x + 7y = 16 \\ 6 \times 3 + 7y = 16 \\ 18 + 7y = 16 \\ 7y = - 2 \\ y = - \frac{2}{7} [/tex]
[tex]3)\left \{ {{4x + 2y = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop {4x - 6y = - 7 \: \: \times ( - 1)}} \right. \\ \\ \left \{ {{4x + 2y = 5} \atop { - 4x + 6y = 7}} \right. + \: \: \: \: \: \: \: \\ 8y = 12 \\ y = 1.5[/tex]
[tex]4x + 2y = 5 \\ 4x + 2 \times 1.5 = 5 \\ 4x + 3 = 5 \\ 4x = 2 \\ x = 0.5[/tex]
[tex]4) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{6x + 7y = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop {3x - 4y = 46 \: \: \times ( - 2)}} \right. \\ \\ \left \{ {{6x + 7y = 2} \atop { - 6x + 8y = - 92}} \right. + \: \: \: \: \: \: \: \: \\ 15y = - 90 \\ y = - 6[/tex]
[tex]6x + 7y = 2 \\ 6x + 7 \times ( - 6) = 2 \\ 6x - 42 = 2 \\ 6x = 44 \\ x = 7 \frac{1}{3} [/tex]
[tex]5) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{2x - 3y = 8 \: \: | \times 5 \: \: \: \: } \atop {7x - 5y = - 5 \: \: | \times ( - 3) }} \right. \\ \\ \left \{ {{10x - 15y = 40} \atop { - 21x + 15y = 15}} \right. + \\ - 11x = 55 \\ x = - 5[/tex]
[tex]2x - 3y = 8 \\ 2 \times ( - 5) - 3y = 8 \\ - 10 - 3y = 8 \\ - 3y = 18 \\ y = - 6[/tex]
[tex]6) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{6x - 7y = 40 \: \: \: \: \: \: \: \: \: \: \: \: } \atop {5y - 2x = - 8 \: \: | \times 3}} \right. \\ \\ \left \{ {{6x - 7y = 40} \atop {15y - 6x = - 24}} \right. + \\ 8y = 16 \\ y = 2[/tex]
[tex]6x - 7y = 40 \\ 6x - 7 \times 2 = 40 \\ 6x - 14 = 40 \\ 6x = 54 \\ x = 9[/tex]
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[tex]1) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{x + y = 4} \atop {x - y = 5}} \right. + \\ 2x = 9 \\ x = 4.5 \\ \\ x + y = 4 \\ 4.5 + y = 4 \\ y = 4 - 4.5 \\ y = - 0.5[/tex]
[tex]2) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{3x - 7y = 11} \atop {6x + 7y = 16}} \right. + \\ 9x = 27 \\ x = 3 \\ \\ 6x + 7y = 16 \\ 6 \times 3 + 7y = 16 \\ 18 + 7y = 16 \\ 7y = - 2 \\ y = - \frac{2}{7} [/tex]
[tex]3)\left \{ {{4x + 2y = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop {4x - 6y = - 7 \: \: \times ( - 1)}} \right. \\ \\ \left \{ {{4x + 2y = 5} \atop { - 4x + 6y = 7}} \right. + \: \: \: \: \: \: \: \\ 8y = 12 \\ y = 1.5[/tex]
[tex]4x + 2y = 5 \\ 4x + 2 \times 1.5 = 5 \\ 4x + 3 = 5 \\ 4x = 2 \\ x = 0.5[/tex]
[tex]4) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{6x + 7y = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop {3x - 4y = 46 \: \: \times ( - 2)}} \right. \\ \\ \left \{ {{6x + 7y = 2} \atop { - 6x + 8y = - 92}} \right. + \: \: \: \: \: \: \: \: \\ 15y = - 90 \\ y = - 6[/tex]
[tex]6x + 7y = 2 \\ 6x + 7 \times ( - 6) = 2 \\ 6x - 42 = 2 \\ 6x = 44 \\ x = 7 \frac{1}{3} [/tex]
[tex]5) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{2x - 3y = 8 \: \: | \times 5 \: \: \: \: } \atop {7x - 5y = - 5 \: \: | \times ( - 3) }} \right. \\ \\ \left \{ {{10x - 15y = 40} \atop { - 21x + 15y = 15}} \right. + \\ - 11x = 55 \\ x = - 5[/tex]
[tex]2x - 3y = 8 \\ 2 \times ( - 5) - 3y = 8 \\ - 10 - 3y = 8 \\ - 3y = 18 \\ y = - 6[/tex]
[tex]6) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \left \{ {{6x - 7y = 40 \: \: \: \: \: \: \: \: \: \: \: \: } \atop {5y - 2x = - 8 \: \: | \times 3}} \right. \\ \\ \left \{ {{6x - 7y = 40} \atop {15y - 6x = - 24}} \right. + \\ 8y = 16 \\ y = 2[/tex]
[tex]6x - 7y = 40 \\ 6x - 7 \times 2 = 40 \\ 6x - 14 = 40 \\ 6x = 54 \\ x = 9[/tex]