Question

How do you solve the system of equations `-3x + 7y = - 9` and `- 2x + 10y = 10`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for `6x`:

-Equation 1:

`-3x + 7y = -9`

`-3x + 7y - color(red)(7y) = -9 - color(red)(7y)`

`-3x + 0 = -9 - 7y`

`-3x = -9 - 7y`

`color(red)(-2) xx -3x = color(red)(-2)(-9 - 7y)`

`6x = (color(red)(-2) xx -9) + (color(red)(-2) xx -7y)`

`6x = 18 + 14y`

-Equation 2:

`-2x + 10y = 10`

`-2x + 10y - color(red)(10y) = 10 - color(red)(10y)`

`-2x + 0 = 10 - 10y`

`-2x = 10 - 10y`

`color(red)(-3) xx -2x = color(red)(-3)(10 - 10y)`

`6x = (color(red)(-3) xx 10) + (color(red)(-3) xx -10y)`

`6x = -30 + 30y`

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

`18 + 14y = -30 + 30y`

`18 + color(red)(30) + 14y - color(red)(14y) = -30 + color(red)(30) + 30y - color(red)(14y)`

`48 + 0 = 0 + 16y`

`48 = 16y`

`48/color(red)(16) = (16y)/color(red)(16)`

`3 = (color(red)(cancel(color(black)(16)))y)/cancel(color(red)(16))`

`3 = y`

`y = 3`

Step 3) Substitute `3` for `y` into either of the equations in Step 1 and solve for `x`:

`6x = -30 + 30y` becomes:

`6x = -30 + (30 xx 3)`

`6x = -30 + 90`

`6x = 60`

`(6x)/color(red)(6) = 60/color(red)(6)`

`(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = 10`

`x = 10`

The Solution Is:

`x = 10` and `y = 3`

Or

`(10, 3)`