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Chapter 4: Problem 44

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 to the system of equations is \(x = 2/3\) and \(y = 1\).

Step by step solution

01

Identify the Substitute

The first equation \(y=3-3x\) is already solved for \(y\), therefore \(y\) can be used as a substitute into the second equation.
02

Perform the Substitution

Substitute \(y\) from the first equation into the second equation, to get \(3x + 4(3-3x) = 6\). Simplify this to \(3x + 12 - 12x = 6\), and further simplifying gives \(-9x + 12 = 6\).
03

Solve For the First Variable

Solve for \(x\) by first subtracting 12 from both sides to get \(-9x = -6\), then divide both sides by \(-9\) to find \(x = 2/3\).
04

Solve for the Second Variable

Substitute \(x = 2/3\) into the first equation \(y = 3 - 3x\) to get \(y = 3 - 3*(2/3)\). This simplifies to \(y = 3 - 2\), so \(y = 1\).

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. If \(x=3, y=2,\) and \(z=-3,\) does the ordered triple \((x, y, z)\) satisfy the equation \(2 x-y+4 z=-8 ?\)

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