How do you solve the linear equation x-y =12 and 2x+y=3 using the substitution method?

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How do you solve the linear equation x-y =12 and 2x+y=3 using the substitution method?

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Answer 1 · 2018-06-11T08:17:23

$(x, y) \to (5, - 7)$ $(x,y)to(5,-7)$

Explanation:

$x - y = 12 \to (1)$ $x-y=12to(1)$

$2 x + y = 3 \to (2)$ $2x+y=3to(2)$

$from equation (2) \to y = 3 - 2 x \to (3)$ $"from equation "(2)toy=3-2xto(3)$

$substitute y = 3 - 2 x into equation (1)$ $color(blue)"substitute "y=3-2x" into equation "(1)$

$x - (3 - 2 x) = 12$ $x-(3-2x)=12$

$x - 3 + 2 x = 12$ $x-3+2x=12$

$add 3 to both sides$ $"add 3 to both sides"$

$3 x = 15$ $3x=15$

$divide both sides by 3$ $"divide both sides by 3"$

$x = \frac{15}{3} = 5$ $x=15/3=5$

$substitute x = 5 into equation (3)$ $"substitute "x=5" into equation "(3)$

$y = 3 - 10 = - 7$ $y=3-10=-7$

$point of intersection = (5, - 7)$ $"point of intersection "=(5,-7)$
graph{(y+2x-3)(y-x+12)((x-5)^2+(y+7)^2-0.04)=0 [-20, 20, -10, 10]}

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How do you solve the linear equation x-y =12 and 2x+y=3 using the substitution method?

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