Question

How do you solve the system of equations `5y = - 6x + 15` and `12x + 10y = - 5`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for `10y`:

• Equation 1:

`5y = -6x + 15`

`2 xx 5y = 2(-6x + 15)`

`10y = (2 xx -6x) + (2 xx 15)`

10y = -12x + 30#

• Equation 2:

`12x + 10y = -5`

`12x - color(12x) + 10y = - color(12x) - 5`

`0 + 10y = -12x - 5`

`10y = -12x - 5`

Step 2) Because the left side of both equations are equal we can equate the right sides of each equation and solve for `x`:

`-12x + 30 = -12x - 5`

`color(red)(12x) - 12x + 30 = color(red)(12x) - 12x - 5`

`0 + 30 = 0 - 5`

`30 != -5`

Because 30 is definitely not equal to -5 we know there are no solutions to this problem. Or, the solution is the null or empty set: `x = {O/}`

This indicates the two lines represented by the equations in the problem are parallel lines and not the same line.