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Solve each system using substitution or elimination. Show all required work. -10x^2+80x+y=155 5x^2-40x+y=-85

Sagot :

MrRoyal

Answer:

[tex]x = 4[/tex]

[tex]y = -5[/tex]

Step-by-step explanation:

Given

[tex]-10x^2+80x+y=155[/tex]

[tex]5x^2-40x+y=-85[/tex]

Required

Solve by substitution

Make y the subject in [tex]5x^2-40x+y=-85[/tex]

[tex]5x^2-40x+y=-85[/tex]

[tex]y = -5x^2 + 40x - 85[/tex]

Substitute [tex]y = -5x^2 + 40x - 85[/tex] in the first equation

[tex]-10x^2+80x+y=155[/tex]

[tex]-10x^2 + 80x -5x^2 + 40x - 85 = 155[/tex]

Collect Like Terms

[tex]-5x^2-10x^2 + 80x + 40x - 85 - 155=0[/tex]

[tex]-15x^2 + 120x-240=0[/tex]

Divide through by -15

[tex]x^2 -8x + 16 = 0[/tex]

[tex]x^2 - 4x - 4x + 16 = 0[/tex]

[tex]x(x - 4) - 4(x - 4) = 0[/tex]

[tex](x - 4)(x - 4) = 0[/tex]

[tex]x - 4\ = 0[/tex] or [tex]x - 4\ = 0[/tex]

[tex]x = 4[/tex] or [tex]x = 4[/tex]

[tex]x = 4[/tex]

Substitute 4 for x in [tex]y = -5x^2 + 40x - 85[/tex]

[tex]y = -5(4)^2 + 40 * 4 - 85[/tex]

[tex]y = -5*16 + 40 * 4 - 85[/tex]

[tex]y = -80 + 160 - 85[/tex]

[tex]y = -5[/tex]

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