Question

Use substitution to solve the following system of equations. - 4y - 5x = 30 AND x= y + 3

Answer 1

Answer:

The solution to the system of equations is y = -5 and x = -2.

Step-by-step explanation:

The question tells us to use substitution to solve the system.  This means that the given value for x (in terms of y) should be substituted into the other equation.  This is modeled below:

-4y - 5x = 30

-4y - 5(y+3) = 30

Next, we should use the distributive property to simplify the left side of the equation.

-4y -5y - 15 = 30

The next step is to combine like terms on the left side of the equation.

-9y - 15 = 30

Then, we can add 15 to both sides of the equation.

-9y = 45

Finally, we can divide both sides of the equation by -9.

y = -5

To find the value for x, we substitute in the value we just found for y into either of our original equations.

x = y + 3

x = -5 + 3

x = -2

Therefore, the correct answer is y = -5 and x = -2.

Hope this helps!