Question

How do you solve the following system: `3x + 4y = 11 , 7x+15y=32`?

Answer 1

`y = 19/17` and `x = 37/17`

Explanation:

Step 1) Solve the first equation for `x`L

`3x + 4y - 4y = 11 - 4y`

`3x + 0 = 11 - 4y`

`3x = 11- 4y`

`(3x)/3 = (11 - 4y)/3`

`1x = (11 - 4y)/3`

`x = 11/3 - (4y)/3`

Step 2) Substitute `11/3 - (4y)/3` for `x` in the second equation and solve for `y`:

`7*(11/3 - (4y)/3) + 15y = 32`

`77/3 - (28y)/3 + 15y = 32`

`77/3 - 77/3 - (28y)/3 + (3/3)*15y = 32 - 77/3`

`(-28y)/3 + (45y)/3 = (3/3)*32 - 77/3`

`(17y)/3 = 96/3 - 77/3`

`(17y)/3 = 19/3`

`(3/17)(17y)/3 = (19/3)(3/17)`

`y = 19/17`

Step 3) Substitute `22/17` for `y` in the solution to the first equation to calculate `x`:

`x = 11/3 - (4/3)(19/17)`

`x = 11/3 - 76/51`

`x = (17/17)(11/3) - 76/51`

`x = 187/51 - 76/51`

`x = 111/51`

`x = (3/3)(37/17)`

`x = 37/17`