Solve the following system by using substitution:
x = -3y - 17
2x + 3y = -7
hmmm. the word "substitution" should give you a clue.
The first equation tells you what x is, so substitute that into the 2nd equation.
2(-3y-17) + 3y = -7
Now solve that for y, and then you can figure out x.
cant find out
To solve the system using substitution, we'll start by solving one of the equations for one variable and then substitute that expression into the other equation.
Let's solve the first equation, x = -3y - 17, for x. To isolate x, we need to get rid of the -17 and the -3y. We can do this by adding 3y and 17 to both sides of the equation:
x + 17 = -3y
or
x = -3y - 17
Now we have an expression for x in terms of y. We will substitute this expression into the second equation, 2x + 3y = -7.
Substituting x with -3y - 17 in the second equation, we get:
2(-3y - 17) + 3y = -7
Simplifying this equation, we distribute the 2 to both terms inside the parentheses:
-6y - 34 + 3y = -7
Combine like terms:
-6y + 3y - 34 = -7
-3y - 34 = -7
Now, let's isolate the variable y by adding 34 to both sides:
-3y = -7 + 34
-3y = 27
Divide both sides by -3 to solve for y:
y = 27 / -3
y = -9
Now that we have the value of y, we can substitute it back into the expression for x that we obtained earlier:
x = -3y - 17
x = -3(-9) - 17
x = 27 - 17
x = 10
Therefore, the solution to the system of equations is x = 10 and y = -9.