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Chapter 7: Problem 68

Explain how to solve a system of equations using the substitution method. Use \(y=3-3 x\) and \(3 x+4 y=6\) to illustrate your explanation.

Short Answer

Expert verified
The solution of the system of equations is \(x = 2/3, y = 1\).

Step by step solution

01

Substitution

Replace \(y\) in the second equation \(3x + 4y = 6\) with the expression from the first equation, \(3 - 3x\), giving us \(3x + 4(3 - 3x) = 6\).
02

Simplify the Equation

Distribute the 4 into the parentheses and simplify to obtain \(3x + 12 - 12x = 6\). Combine like terms to get \(-9x + 12 = 6\).
03

Solve for x

To solve for \(x\), first subtract 12 from both sides to get \(-9x = -6\). Then divide each side by -9 to solve for \(x\), giving us \(x = 2/3\).
04

Solve for y

Substitute \(x = 2/3\) into the first equation \(y = 3 - 3x\) to solve for \(y\), giving us \(y = 3 - 3 * (2/3) = 3 - 2 = 1\).

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