How do you solve the following linear system: $- x + 4 y = - 8, 3 x + 2 y = 9$ $-x + 4y = -8 , 3x + 2y = 9$ ?

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How do you solve the following linear system: $- x + 4 y = - 8, 3 x + 2 y = 9$ $-x + 4y = -8 , 3x + 2y = 9$ ?

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Answer 1 · 2015-11-14T00:10:32

Substitution.

Explanation:

Substitution Method
Solve for $x$ $x$ in the equation $- x + 4 y = - 8$ $-x + 4y = -8$ .

Subtract $4 y$ $4y$ from both sides: $- x = - 4 y - 8$ $-x = -4y - 8$
Divide both sides by $- 1$ $-1$ : $x = 4 y + 8$ $x = 4y + 8$
Now, knowing that $x = 4 y + 8$ $x = 4y + 8$ , replace $x$ $x$ in the other equation with $4 y + 8$ $4y + 8$ .

This gives: $3 (4 y + 8) + 2 y = 9$ $3(4y + 8) + 2y = 9$
Distribute: $12 y + 24 + 2 y = 9$ $12y + 24 + 2y = 9$
Combine like terms on the left side: $14 y + 24 = 9$ $14y + 24 = 9$
Subtract $24$ $24$ from both sides: $14 y = - 15$ $14y = -15$
Divide both sides by $14$ $14$ : $y = - \frac{15}{14}$ $color(red)(y = -15/14)$

Now, plug in your new value for $y$ $y$ in either equation.
Example: $3 x + 2 (- \frac{15}{14}) = 9$ $3x + 2(-15/14) = 9$
Multiply: $3 x + (- \frac{30}{14}) = 9$ $3x + (-30/14) = 9$
Simplify: $3 x - \frac{15}{7} = 9$ $3x - 15/7 = 9$
Add $\frac{15}{7}$ $15/7$ to both sides and find a common denominator: $3 x = \frac{15}{7} + \frac{63}{7}$ $3x = 15/7 + 63/7$
Add: $3 x = \frac{78}{7}$ $3x = 78/7$
Divide both sides by $3$ $3$ : $x = \frac{78}{15}$ $x = 78/15$
Simplify: $x = \frac{26}{5}$ $color(red)(x = 26/5)$

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How do you solve the following linear system: $- x + 4 y = - 8, 3 x + 2 y = 9$ $-x + 4y = -8 , 3x + 2y = 9$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the following linear system: −x+4y=−8,3x+2y=9-x + 4y = -8 , 3x + 2y = 9 ?

1 Answer

Explanation:

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Impact of this question

How do you solve the following linear system: $- x + 4 y = - 8, 3 x + 2 y = 9$ $-x + 4y = -8 , 3x + 2y = 9$ ?