Question

Solve the following system by elimination. x-(1)/(5)y=5 -x+(2)/(3)y=-(50)/(3)

Answer 1

The system of equations is solved by elimination to find x = -9 and y = -70. We first aligned the coefficients of x by multiplying the equations, then added them to eliminate x and found y. After substituting y into one of the original equations, we found x.

Step-by-step explanation:

To solve the system of equations by elimination, we need to add or subtract the equations to eliminate one of the variables.

The given system is:

1. x - ⅔y = 5
2. -x + ¾xy = -⅖50

Multiply the first equation by 3 and the second by 5 to get common coefficients for x:

1. 3x - ⅔(3)y = 15
2. -5x + ¾x(5)y = -50

By adding these new equations, the x terms will cancel out:

3x - ⅔(3)y + (-5x + ¾x(5)y) = 15 - 50

This simplifies to:

¾(2)y = -35

Solve for y:

y = -35 / (¾(2))

y = -35 / (¾x2)

y = -35 / ⅖

y = -35 * ⅖

y = -210/3

y = -70

Substitute y = -70 into one of the original equations to solve for x:

x - ⅔(-70) = 5

x + 14 = 5

x = 5 - 14

x = -9

The solution to the system is x = -9, y = -70.