Question

substitution. add the values of x and y and the sum is ______.
2x - 4y = 12
3x + 4y = 8

a. -3 b. 19 c. no solution d. 3

Explanation:

Step1: Solve the system of equations

We have the system:

$$
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$$

Add the two equations together to eliminate \(y\):
\((2x - 4y)+(3x + 4y)=12 + 8\)
Simplify the left side: \(2x-4y + 3x + 4y=5x\)
Simplify the right side: \(20\)
So we get \(5x=20\), then solve for \(x\) by dividing both sides by \(5\): \(x=\frac{20}{5}=4\)

Step2: Find the value of \(y\)

Substitute \(x = 4\) into the second equation \(3x+4y = 8\):
\(3\times4+4y=8\)
Simplify: \(12 + 4y=8\)
Subtract \(12\) from both sides: \(4y=8 - 12=-4\)
Divide both sides by \(4\): \(y=\frac{-4}{4}=-1\)

Step3: Calculate the sum of \(x\) and \(y\)

The sum of \(x\) and \(y\) is \(x + y=4+(-1)=3\)

Answer:

d. 3