Question

Solve the following system hood equations by the substitution method

Answer 1

Question:

Solution:

Consider the following system of linear equations:

Equation 1:

$6x+7y=17$

Equation 2:

$x=22-5y$

Replacing the above equation into equation 1, we get:

$6(22-5y)+7y=17$

Applying the distributive property, we get:

$132-30y+7y=17$

this is equivalent to:

$-30y+7y=17-132$

this is equivalent to:

$-23y=\text{ -115}$

or

$23y=\text{ 115}$

solving for y, we obtain:

$y=\frac{115}{23}=5$

Now, replacing this into Equation 2, we obtain:

$x=22-5(5)=22-25=-3$

So that, we can conclude that the correct answer is:

The solution is (-3, 5)