Answer:
See explanation for matching pairs
Step-by-step explanation:
Equations
(1)
[tex]x - y = 25[/tex]
[tex]2x + 3y = 180[/tex]
(2)
[tex]2x - 3y = -5[/tex]
[tex]11x + y = 550[/tex]
(3)
[tex]x - y = 19[/tex]
[tex]-12x + y = 168[/tex]
Solutions
[tex](-17,-36)[/tex]
[tex](47, 33)[/tex]
[tex](51, 26)[/tex]
Required
Match equations with solutions
(1) [tex]x - y = 25[/tex] and [tex]2x + 3y = 180[/tex]
Make x the subject in: [tex]x - y = 25[/tex]
[tex]x = 25 + y[/tex]
Substitute [tex]x = 25 + y[/tex] in [tex]2x + 3y = 180[/tex]
[tex]2(25 + y) + 3y = 180[/tex]
[tex]50 + 2y + 3y = 180[/tex]
[tex]50 + 5y = 180[/tex]
Collect like terms
[tex]5y = 180-50[/tex]
[tex]5y = 130[/tex]
Solve for y
[tex]y =26[/tex]
Recall that: [tex]x = 25 + y[/tex]
[tex]x = 25 + 26[/tex]
[tex]x = 51[/tex]
So:
[tex](x,y) = (51,26)[/tex]
(2) [tex]2x - 3y = -5[/tex] and [tex]11x + y = 550[/tex]
Make y the subject in [tex]11x + y = 550[/tex]
[tex]y = 550 - 11x[/tex]
Substitute [tex]y = 550 - 11x[/tex] in [tex]2x - 3y = -5[/tex]
[tex]2x - 3(550 - 11x) = -5[/tex]
[tex]2x - 1650 + 33x = -5[/tex]
Collect like terms
[tex]2x + 33x = -5+1650[/tex]
[tex]35x = 1645[/tex]
Solve for x
[tex]x = 47[/tex]
Solve for y in [tex]y = 550 - 11x[/tex]
[tex]y = 550 - 11 * 47[/tex]
[tex]y = 550 - 517[/tex]
[tex]y = 33[/tex]
So:
[tex](x,y) = (47,33)[/tex]
(3)
[tex]x - y = 19[/tex] and [tex]-12x + y = 168[/tex]
Make y the subject in [tex]-12x + y = 168[/tex]
[tex]y = 168 + 12x[/tex]
Substitute [tex]y = 168 + 12x[/tex] in [tex]x - y = 19[/tex]
[tex]x - 168 - 12x = 19[/tex]
Collect like terms
[tex]x -12x = 168 + 19[/tex]
[tex]-11x = 187[/tex]
Solve for x
[tex]x = -17[/tex]
Solve for y in [tex]y = 168 + 12x[/tex]
[tex]y =168-12 *17[/tex]
[tex]y =-36[/tex]
So:
[tex](x,y) = (-17,-36)[/tex]
