Answer:
Explanation:
To solve the given system of equations using the addition method, we want to eliminate one variable by adding or subtracting the equations. Let's begin by multiplying both sides of the first equation by 3 to eliminate the fraction: 3 * (5x + y/3) = 3 * (2/3) 15x + y = 2 Next, let's simplify the second equation by multiplying both sides by 6 to eliminate the fraction: 6 * (6 / (2x 3) - y / 2) = 6 * (23 / 6) 36 / (2x 3) - 6y / 2 = 23 18 / (2x 3) - 3y = 23 Now we have the following system of equations: 15x + y = 2 18 / (2x 3) - 3y = 23 To eliminate the fractions, we can multiply both sides of the second equation by (2x 3): (2x 3) * (18 / (2x 3) - 3y) = (2x 3) * 23 18 - 6y(2x 3) = 46x 3 18 - 6y = 46x - 9y Combining like terms, we have: 46x - 9y = 18 - 6y Now we can rewrite the system of equations as: 15x + y = 2 46x - 9y = 18 - 6y To eliminate the y term, we can multiply the first equation by 9 and the second equation by 1: 9 * (15x + y) = 9 * 2 1 * (46x - 9y) = 1 * (18 - 6y) Simplifying, we get: 135x + 9y = 18 46x - 9y = 18 - 6y Now, add the two equations together: 135x + 9y + 46x - 9y = 18 + (18 - 6y) 181x = 36 Divide both sides by 181 to solve for x: x = 36 / 181 x ≈ 0.199 Substitute this value of x back into one of the original equations, let's use the first equation, to solve for y: 15(0.199) + y = 2 2.985 + y = 2 y = 2 - 2.985 y ≈ -0.985 Therefore, the solution to the given system of equations is approximately x ≈ 0.199 and y ≈ -0.985.