How do you solve the following linear system: $6 x + y = 3, 2 x + 3 y = 5$ $6x+y =3, 2x+3y=5$ ?

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How do you solve the following linear system: $6 x + y = 3, 2 x + 3 y = 5$ $6x+y =3, 2x+3y=5$ ?

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Answer 1 · 2018-03-04T10:58:14

$x = \frac{1}{4}, y = \frac{3}{2}$ $x=1/4, y=3/2$

Explanation:

In this case, we can use substitution, but I find using elimination simpler. We can see that if we do a little work, subtracting the two equations will let us solve for $y$ $y$ .

$E_{1} : 6 x + y = 3$ $E_1: 6x+y=3$

$E_{2} : 2 x + 3 y = 5$ $E_2: 2x+3y=5$

$E_{2} : 3 (2 x + 3 y) = 3 \cdot 5$ $E_2: 3(2x+3y)=3*5$

$E_{2} : 6 x + 9 y = 15$ $E_2: 6x+9y=15$

$E_{1} - E_{2} : 6 x + y - (6 x + 9 y) = 3 - 15$ $E_1-E_2: 6x+y-(6x+9y)=3-15$

$6 x - 6 x + y - 9 y = - 12$ $6x-6x+y-9y=-12$

$- 8 y = - 12$ $-8y=-12$

$y = \frac{- 12}{- 8} = \frac{3}{2}$ $y=(-12)/(-8)=3/2$

Now we plug in the solution to $y$ $y$ into $E_{1}$ $E_1$ to solve for $x$ $x$ :

$E_{1} : 6 x + \frac{3}{2} = 3$ $E_1: 6x+3/2=3$

$6 x = 3 - \frac{3}{2}$ $6x=3-3/2$

$6 x = \frac{3}{2}$ $6x=3/2$

$x = \frac{\frac{3}{2}}{6} = \frac{3}{12} = \frac{1}{4}$ $x=(3/2)/6=3/12=1/4$

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How do you solve the following linear system: $6 x + y = 3, 2 x + 3 y = 5$ $6x+y =3, 2x+3y=5$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the following linear system: 6x+y=3,2x+3y=5 6x+y =3, 2x+3y=5 ?

1 Answer

Explanation:

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Impact of this question

How do you solve the following linear system: $6 x + y = 3, 2 x + 3 y = 5$ $6x+y =3, 2x+3y=5$ ?