Question

Solve the system by the substitution method 8x-3y=-22 and y=5x+19

Answer 1

The answer is: $x=-5\\y=-6$

The explanation is shown below:

1. In substitution method you can solve one of the equation for one of the variables, then you must substitute it into the other equation and solve it to calculate the other variable. Once you do this, you must substitute the value obtained into one of the original equations to calculate the second variable.

2. Keeping this on mind, you can see that the second equation is already solved for $y$. Therefore, you can substitute this into the first one and solve for $x$:

$8x-3y=-22\\8x-3(5x+19)=-22\\8x-15x-57=-22\\-7x=35\\x=-5$

3. Let's substitute the value obtained into the second equation to calculate $y$:

$y=5x+19\\y=5(-5)+19\\y=-6$

4. The result is:

$x=-5\\y=-6$