Question

Let's look at this system of equations:

2x - 4y = 10
X + 5y = 40
Solve the system using substitution or elimination.

Answer 1

To solve the system of equations using elimination or substitution method, multiply the second equation by 2 and subtract it from the first equation to eliminate x. Simplify and solve for y, then substitute the value of y back into one of the original equations to find x. The solution is x = 15 and y = 5.

Step-by-step explanation:

To solve the system of equations: 2x - 4y = 10 and x + 5y = 40, we can use the method of elimination or substitution.

Elimination:

1. Multiply the second equation by 2 to make the coefficient of x the same as the first equation: 2(x + 5y) = 2(40) ➞ 2x + 10y = 80.
2. Subtract the first equation from the modified second equation to eliminate x: (2x + 10y) - (2x - 4y) = 80 - 10.
3. Simplify: 14y = 70.
4. Divide both sides by 14: y = 5.
5. Substitute the value of y back into either of the original equations to solve for x: x + 5(5) = 40 ➞ x + 25 = 40 ➞ x = 15.

Therefore, the solution to the system of equations is x = 15 and y = 5.