How do you solve the system $3 x - 2 y = 11$ $3x-2y=11$ and $x - \frac{1}{2} y = 4$ $x-1/2y=4$ using substitution?

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How do you solve the system $3 x - 2 y = 11$ $3x-2y=11$ and $x - \frac{1}{2} y = 4$ $x-1/2y=4$ using substitution?

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Answer 1 · 2017-09-05T18:43:23

$(x, y) \to (5, 2)$ $(x,y)to(5,2)$

Explanation:

$3 x - 2 y = 11 \to (1)$ $3x-2y=11to(1)$

$x - \frac{1}{2} y = 4 \to (2)$ $x-1/2y=4to(2)$

$from (2) x x = 4 + \frac{1}{2} y \to (3)$ $"from "(2)color(white)(x)x=4+1/2yto(3)$

$substitute x = 4 + \frac{1}{2} y into (1)$ $"substitute "x=4+1/2y" into "(1)$

$3 (4 + \frac{1}{2} y) - 2 y = 11$ $3(4+1/2y)-2y=11$

$\Rightarrow 12 + \frac{3}{2} y - 2 y = 11$ $rArr12+3/2y-2y=11$

$\Rightarrow - \frac{1}{2} y = - 1$ $rArr-1/2y=-1$

$\Rightarrow y = 2$ $rArry=2$

$substitute this value into (3)$ $"substitute this value into "(3)$

$\Rightarrow x = 4 + 1 = 5$ $rArrx=4+1=5$

$\Rightarrow point of intersection = (5, 2)$ $rArr"point of intersection "=(5,2)$
graph{(y-3/2x+11/2)(y-2x+8)((x-5)^2+(y-2)^2-0.04)=0 [-10, 10, -5, 5]}

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How do you solve the system $3 x - 2 y = 11$ $3x-2y=11$ and $x - \frac{1}{2} y = 4$ $x-1/2y=4$ using substitution?

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Explanation:

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How do you solve the system $3 x - 2 y = 11$ $3x-2y=11$ and $x - \frac{1}{2} y = 4$ $x-1/2y=4$ using substitution?