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frez [133]
2 years ago
12

X+y=3 2x-y=0 substituition method

Mathematics
1 answer:
Veronika [31]2 years ago
5 0

Answer:

(1, 2 )

Step-by-step explanation:

x + y = 3 (subtract x from both sides )

y = 3 - x → (1)

2x - y = 0 → (2)

Substitute y = 3 - x into (2)

2x - (3 - x) = 0

2x - 3 + x = 0

3x - 3 = 0 ( add 3 to both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Substitute x = 1 into (1)

y = 3 - 1 = 2

solution is (1, 2 )

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Step-by-step explanation:

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\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}

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