How do you solve the linear equation x+3y=2 and -x+y=1 using the substitution method and are they dependent, independent, or inconsistent?

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How do you solve the linear equation x+3y=2 and -x+y=1 using the substitution method and are they dependent, independent, or inconsistent?

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Answer 1 · 2017-10-22T22:28:19

$x = - (\frac{1}{4}), y = (\frac{3}{4})$ $x = -(1/4), y = (3/4)$
They are dependent and consistent.

Explanation:

$x + 3 y = 2$ $x + 3y = 2$
#x = 2 - 3y color(white)(aaa) Eqn (2)

$- x + y = 1 a a a$ $-x + y = 1 color (white)(aaa)$ Eqn (1),

Substituting value of “x “ in Eqn (1),

$- (2 - 3 y) + y = 1$ $-(2-3y) + y = 1$

$3 y + y = 3$ $3y + y = 3$
$4 y = 3, or y = \frac{3}{4}$ $4y = 3, or y = 3/4$

Substituting value of “y” in Eqn (1),

$- x + (\frac{3}{4}) = 1$ $-x + (3/4) = 1$
$- x = \frac{1}{4}, or x = - \frac{1}{4}$ $-x = 1/4, or x = -1/4$

Verification :
Substituting value of “y” in Eqn (2),
$x = 2 - 3 y = 2 - 3 (\frac{3}{4}) = 2 - 2 (\frac{1}{4}) = - (\frac{1}{4})$ $x = 2 - 3y = 2 - 3(3/4) = 2 - 2(1/4) = -(1/4)$

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How do you solve the linear equation x+3y=2 and -x+y=1 using the substitution method and are they dependent, independent, or inconsistent?

1 Answer

Explanation:

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