How do solve the following linear system?: $6 x = 29 - 8 y, 3 y = 1 - x$ $6x=29-8y , 3y = 1 -x$ ?

Question

How do solve the following linear system?: $6 x = 29 - 8 y, 3 y = 1 - x$ $6x=29-8y , 3y = 1 -x$ ?

2 Answers

Impact of this question

2041 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-09T23:48:38

The solution is a point at $x = 7.9$ $x=7.9$ and $y = - 2.3$ $y=-2.3$

Explanation:

Substitution implies that we solve for either $x$ $x$ or $y$ $y$ in one equation and substitute that into the other. I see a lonely $x$ $x$ in the second equation that should be easy to solve for, so I'll start there:

$3 y = 1 - x$ $3y=1-x$

$x = 1 - 3 y$ $x = 1-3y$

Then we substitute $1 - 3 y$ $1-3y$ for $x$ $x$ in the first equation:

$6 (1 - 3 y) = 29 - 8 y$ $6(1-3y)=29-8y$

$8 y - 18 y = 29 - 6$ $8y-18y = 29 - 6$

$- 10 y = 23$ $-10y = 23$

$y = - 2.3$ $y = -2.3$

Then we can use our original solution for $x$ $x$ to get

$x = 1 - 3 y = 1 - 3 \cdot (- 2.3) = 7.9$ $x = 1- 3y = 1-3*(-2.3) = 7.9$

check:

eq1:

$6 x = 29 - 8 y$ $6x = 29 - 8y$

$6 \cdot (7.9) = 29 - 8 \cdot (- 2.3)$ $6*(7.9) = 29-8*(-2.3)$

$47.4 = 47.4 \Rightarrow t r u e$ $47.4 = 47.4 \implies true$

eq2:

$3 y = 1 - x$ $3y = 1-x$

$3 \cdot (- 2.3) = 1 - 7.9$ $3*(-2.3) = 1-7.9$

$- 6.9 = - 6.9 \Rightarrow t r u e$ $-6.9 = -6.9 \implies true$

Answer 2 · 2018-03-10T02:43:04

$x = \frac{79}{10}$ $color(green)( x = (79)/10$

$y = - \frac{23}{10}$ $color(green)(y=-23/10$

Explanation:

Given:

$6 x = 29 - 8 y, 3 y = 1 - x$ $color(red)(6x=29-8y , 3y = 1 -x$

Write the equations separately:

$6 x = 29 - 8 y$ $6x=29-8y$ Equation (1)

$3 y = 1 - x$ $3y = 1 -x$ Equation (2)

Consider

$6 x = 29 - 8 y$ $6x=29-8y$ Equation (1)

Add $8 y$ $color(blue)(8y$ to both sides of the equation.

$6 x + 8 y = 29 - 8 y + 8 y$ $6x + color(blue)(8y)=29-8y+color(blue)(8y)$

$6x + color(blue)(8y)=29cancel(-8y)color(blue)cancel(+8y)$

$color(blue)(6x + 8y = 29)$ Equation (3)

Consider

$3y = 1 -x$ Equation (2)

Add $color(blue)(x$ to both sides of the equation.

$3y + color(blue)(x) = 1 -x+color(blue)(x$

$3y + color(blue)(x) = 1 -cancel(x)+color(blue)(cancel(x)$

$color(blue)(x + 3y = 1)$ Equation (4)

Consider:

$color(blue)(6x + 8y = 29)$ Equation (3)

$color(blue)(x + 3y = 1)$ Equation (4)

Multiply both sides of the Equation (4) by 6.

This resultant equation is Equation (5)

$color(blue)(6x + 8y = 29)$ Equation (3)

$color(blue)(6x + 18y = 6)$ Equation (5)

Subtract Equation (5) from Equation (3)

$cancel(6x) + 8y = 29$ Equation (3)

$-cancel(6x) - 18y = -6$ Equation (5)

You get

$-10y=23$

Divide both sides by 10 to get

$(-cancel(10)y)/cancel(10)=23/10$

$=-y = 23/10$

Multiply both sides by $(-1)$ to get

$=(-y)(-1) = (23/10)(-1)$

$color(green)(y=-23/10$

Substitute this value of $y$ in $color(blue)(x + 3y = 1)$ Equation (4) to get

$x+3(-23/10) = 1$

$rArr x-69/10 = 1$

Add $69/10$ to both the sides to get

$rArr x-69/10 + 69/10 = 1+69/10$

$rArr x-cancel(69/10) + cancel(69/10) = 1+69/10$

$rArr x = 1+69/10$

Take the common denominator of the numeric expression at the Right-Hand Side(RHS) to simplify:

$rArr x = (10+69)/10$

$color(green)( x = (79)/10$

Hence, values of $x and y$ are:

$color(green)( x = (79)/10$

$color(green)(y=-23/10$

The system of linear equations is solved.

Science

Math

Humanities

... and beyond

How do solve the following linear system?: $6 x = 29 - 8 y, 3 y = 1 - x$ $6x=29-8y , 3y = 1 -x$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do solve the following linear system?: 6x=29-8y , 3y = 1 -x 6x=29−8y,3y=1−x 6x=29-8y , 3y = 1 -x ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do solve the following linear system?: $6 x = 29 - 8 y, 3 y = 1 - x$ $6x=29-8y , 3y = 1 -x$ ?