Solve the system of equations by substitution and
explain all your steps in words:
3x + y = 12
x = y − 8 .
Is this a good way to explain this problem?
Step 1: Since X is given to us. We can plug it into the x-value in the first equation. x= y-8 into 3x+y=12
3(y-8)=12. Distribute to solve for your new equation.
3y-24=12. Add 24 to both sides to get 3y by itself.
3y=36. Divide by 3
3y/3=36/3. Y=12.
I have never seen a math problem like this. Its always been have the equation or whatever. Solve for blah blah
what happened to the y that was already in the 1st equation?
oh snaps I left it out. It should be 3y-24+y=12 should turn into 4y-24=12. its still 36=4y
y=9 now. Thanks Scott
Yes, your explanation is a good way to approach this problem using substitution. Let's break down the steps:
Step 1: Since the equation x = y - 8 is given to us, we can substitute this expression for x in the first equation, 3x + y = 12. So, we replace x with y - 8:
3(y - 8) + y = 12.
Step 2: Now we distribute the 3 to both terms inside the parentheses:
3y - 24 + y = 12.
Step 3: Combine like terms by adding y and 3y:
4y - 24 = 12.
Step 4: To isolate the variable, we need to move -24 to the other side of the equation. We do this by adding 24 to both sides:
4y - 24 + 24 = 12 + 24.
Simplifying gives us:
4y = 36.
Step 5: We divide both sides by 4 to solve for y:
4y/4 = 36/4,
y = 9.
Therefore, the solution to the system of equations is y = 9.
To find the value of x, we substitute the value of y back into one of the original equations. Let's use x = y - 8:
x = 9 - 8,
x = 1.
Thus, the solution to the system of equations is x = 1 and y = 9.