Solve the system of equations using substitution.
x + 4y = -5
3x - 8y = 45
When I tried to solve it, I got x=-17 and y=-3. When I plugged these into the first equation, it didn't work out at all. Could someone please show me the steps so I can see where I went wrong? Thank you!
I doubled the first and added it to the second to get
5x = 35,
so x = 7, subbing that back I got y = -3
those values verify.
MC-- 7th grade algebra.
Thanks for your help, Reiny!
since you need to solve the system of equations by substitution, solve the first equation for x by subtracting 4y from both sides. You will get x = -5 - 4y.
Next substitute this expression into the x of the 2nd equation to get
3(-5 - 4y)- 8y =45
Now use the distributive property to get
-15 -12y - 8y =45
simplify to get
-15 -20y = 45 (when you combine to negatives you get a negative answer)
add 15 to both sides and you get
-20y = 60
divide both sides by -20 to get y = -3.
Now replace this answer into the first equation or the x = -5 - 4y equation to get x= -5 - 4(-3) = -5 + 12 = 7
answer (7,-3)
To solve the system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation. Let's start with the first equation:
1) x + 4y = -5
We can solve this equation for x in terms of y:
2) x = -5 - 4y
Now, substitute equation 2) into the second equation:
3) 3(-5 - 4y) - 8y = 45
Simplify the equation:
4) -15 - 12y - 8y = 45
Combine like terms:
5) -15 - 20y = 45
Add 15 to both sides:
6) -20y = 60
Divide both sides by -20:
7) y = -3
Now that we have the value of y, substitute it back into equation 2) to find x:
8) x = -5 - 4(-3)
= -5 + 12
= 7
Therefore, the solution to the system of equations is x = 7 and y = -3.
It seems that you made an error when substituting the values of x and y into the first equation. Let's check if the values we found satisfy the first equation:
x + 4y = -5
7 + 4(-3) = -5
7 - 12 = -5
-5 = -5
As we can see, the solution satisfies the first equation, which confirms that our answer is correct.