Question

How do you solve the following linear system: `-9 y + 2x = 2 , 5x - y = 3`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the second equation for `y`:

`5x - y = 3`

`-color(red)(3) + 5x - y + color(blue)(y) = -color(red)(3) + 3 + color(blue)(y)`

`-3 + 5x - 0 = 0 + color(blue)(y)`

`-3 + 5x = y`

`y = -3 + 5x`

Step 2) Substitute `(-3 + 5x)` for `y` in the first equation and solve for `x`:

`-9y + 2x = 2` becomes:

`-9(-3 + 5x) + 2x = 2`

`(-9 xx -3) + (-9 xx 5x) + 2x = 2`

`27 - 45x + 2x = 2`

`27 + (-45 + 2)x = 2`

`27 - 43x = 2`

`-color(red)(27) + 27 - 43x = -color(red)(27) + 2`

`0 - 43x = -25`

`-43x = -25`

`(-43x)/color(red)(-43) = (-25)/color(red)(-43)`

`(color(red)(cancel(color(black)(-43)))x)/cancel(color(red)(-43)) = 25/43`

`x = 25/43`

Step 3) Substitute `25/43` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = -3 + 5x` becomes:

`y = -3 + (5 xx 25/43)`

`y = -3 + 125/43`

`y = (-3 xx 43/43) + 125/43`

`y = -129/43 + 125/43`

`y = -4/43`

The solution is: `x = 25/43` and `y = -4/43` or `(25/43, -4/43)`

Answer 2

`x=25/43, y=-4/43.`

Explanation:

From the second eqn., `5x-3=y.`

Subst.ing this value of `y` in the first eqn., we get,

`-9(5x-3)+2x=2.`

`:. -45x+27+2x=2.`

`:. -43x=2-27=-25.`

`:. x=25/43.`

`:. y=5x-3=5(25/43)-3=125/43-3=(125-129)/43.`

`;. y=-4/43.`

Hence, the Soln. `x=25/43, y=-4/43.`