Solve the following system of equations using the Addition/Elimination method: \(3x - 2y = 4\) and \(2x + 3y = -1\)
Answer
We solve for y by adding 2y to both sides and then dividing by -2: \(y = (30 / 13 - 4) / 2\). This simplifies to: \(y = -4 / 13\)
Step 1 ：First, we multiply the first equation by 3 and the second equation by 2 to ensure that the coefficients of y's in both equations will cancel out when summed: \(3 * (3x - 2y) = 3 * 4\) and \(2 * (2x + 3y) = 2 * -1\). This results in: \(9x - 6y = 12\) and \(4x + 6y = -2\)
Step 2 ：Next, we add the two equations together: \((9x - 6y) + (4x + 6y) = 12 - 2\). This simplifies to: \(13x = 10\)
Step 3 ：Finally, we solve for x by dividing both sides of the equation by 13: \(x = 10 / 13\)
Step 4 ：Substitute x = 10 / 13 into the first equation: \(3 * (10 / 13) - 2y = 4\). This simplifies to: \(30 / 13 - 2y = 4\)
Step 5 ：We solve for y by adding 2y to both sides and then dividing by -2: \(y = (30 / 13 - 4) / 2\). This simplifies to: \(y = -4 / 13\)
