Problem

Solve the following system of equations using the substitution method: \(2x + 3y = 12\) and \(x = y + 4\)

Answer

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Answer

Simplify to get the value of x: \(x = \frac{24}{5}\)

Steps

Step 1 ：First, substitute the second equation into the first, to get: \(2(y + 4) + 3y = 12\)

Step 2 ：This simplifies to: \(2y + 8 + 3y = 12\)

Step 3 ：Which further simplifies to: \(5y + 8 = 12\)

Step 4 ：Subtracting 8 from both sides, we get: \(5y = 4\)

Step 5 ：Dividing both sides by 5, we find that: \(y = \frac{4}{5}\)

Step 6 ：Substitute \(y = \frac{4}{5}\) back into the second equation to find x: \(x = \frac{4}{5} + 4\)

Step 7 ：Simplify to get the value of x: \(x = \frac{24}{5}\)

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