Question

X-4y=5 3x+2y=29 solve for x and y

Answer 1

To solve the system of equations x - 4y = 5 and 3x + 2y = 29, use the elimination method to find x = 9 and y = 1 as the solution.

Step-by-step explanation:

The system of equations to be solved is:

• x - 4y = 5
• 3x + 2y = 29

To solve the system of equations, you can use either substitution or elimination. The elimination method is often more straightforward when the equations are already aligned with coefficients that are conducive to eliminating one of the variables.

Let's multiply the first equation by 2 to make the coefficients of y opposites:

1. 2(x - 4y) = 2(5) → 2x - 8y = 10
2. 3x + 2y = 29

Now, add the equations together:

• (2x - 8y) + (3x + 2y) = 10 + 29
• 5x - 6y = 39

Then, you can easily calculate the value of x:

• 5x = 39 + 6y
• x = (39 + 6y) / 5

Insert x back into one of the original equations:

• (39 + 6y)/5 - 4y = 5
• 39 + 6y - 20y = 25
• -14y = -14
• y = 1

Finally, solve for x using the value of y:

• x - 4(1) = 5
• x - 4 = 5
• x = 9

Therefore, the solution to the system of equations is x = 9 and y = 1.