Question

Solve the system using elimination.5x + 4y = 123x – 3y = 18

Answer 1

To solve the system using elimination, we need to eliminate one of the variables by manipulating the equations.

To eliminate x, we need to multiply the second equation by 5 and the first equation by 3:

3(5x + 4y) = 3(123)
5(3x - 3y) = 5(18)

Simplifying:
15x + 12y = 369
15x - 15y = 90

Now, we can subtract the second equation from the first equation:
(15x + 12y) - (15x - 15y) = 369 - 90
15x + 12y - 15x + 15y = 279

Simplifying further:
27y = 279

Dividing both sides of the equation by 27:
y = 279/27
y = 9

Substituting the value of y into one of the original equations, let's use the first equation:
5x + 4(9) = 123
5x + 36 = 123
5x = 123 - 36
5x = 87
x = 87/5

Therefore, the solution to the system of equations is x = 87/5 and y = 9.