Answer:
1) [tex]{y,x}={2,-2}[/tex]
2) [tex]{y,x} = {-4,-2}[/tex]
Step-by-step explanation:
1) [tex]y=x+4 \\ 5x+3y=-4[/tex] <---------- given linear equations
Equations Simplified or Rearranged :
[tex]y - x = 4 \\3y + 5x = -4[/tex]
Graphic Representation of the Equations : PICTURE #1
[tex]x + y = 4 \\5x + 3y = -4[/tex]
Solve by Substitution :
// Solve equation [1] for the variable y
[tex][1] y = x + 4[/tex]
// Plug this in for variable y in equation [2]
[tex]3*(x +4) + 5x = -4 \\ [2] 8x = -16[/tex]
// Solve equation [2] for the variable x
[tex]8x = - 16 x = - 2[/tex]
// By now we know this much :
[tex]y = x+4\\ x = -2[/tex]
// Use the x value to solve for y
[tex]y = (-2)+4 = 2[/tex]
Solution :
[tex]{y,x} = {2,-2}[/tex]
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2) [tex]y=2x \\-8x-2y=24[/tex] <----- linear equations given
Equations Simplified or Rearranged :
[tex]y - 2x = 0 \\ -2y - 8x = 24[/tex]
Graphic Representation of the Equations : PICTURE #2
[tex]-2x + y = 0 \\\\-8x - 2y = 24[/tex]
Solve by Substitution :
// Solve equation [1] for the variable y
[tex][1] y = 2x[/tex]
// Plug this in for variable y in equation [2]
[tex][2] -2*(2x) - 8x = 24\\ [2] - 12x = 24[/tex]
// Solve equation [2] for the variable x
[tex][2] 12x = - 24 [2] x = - 2[/tex]
// By now we know this much :
[tex]y = 2x \\ x = -2[/tex]
// Use the x value to solve for y
[tex]y = 2(-2) = -4[/tex]
Solution :
[tex]{y,x} = {-4,-2}[/tex]
