I'm really confused on substitution. My teacher has a terrible accent and cannot understand what she says. i get the basics myself but i'm pretty confused on the following problems:
1) y= 3x - 8
y= 4-x
2) 2x + 7y = 3
x=1- 4y
3) x = 2y
4x + 2y = 15
Any help. I know i should probably know this by now. i started mid term :/
3. Substitute 2y for x in the second equation.
4(2y) + 2y = 15
Solve for y. Put that value in the first equation to solve for x. Check by putting both values in the second equation.
You can substitute either x or y value from one equation to the other to solve.
Use these steps in doing the first two problems. I hope this helps.
I can understand your frustration, but don't worry! I'll explain the concept of substitution and guide you step-by-step through each problem.
Substitution is a useful method to solve a system of equations by expressing one variable in terms of the other and substituting that expression into the other equation. This allows us to solve for the remaining variable.
Let's go through each problem one by one:
1) y = 3x - 8
y = 4 - x
To solve this system, we need to substitute the value of y in terms of x from one equation into the other equation. Since both equations have y isolated, we can equate the right sides:
3x - 8 = 4 - x
Now, solve for x:
3x + x = 4 + 8
4x = 12
x = 3
Next, substitute the value of x into either equation to find y. Let's use the first equation:
y = 3(3) - 8
y = 9 - 8
y = 1
Therefore, the solution to this system is x = 3 and y = 1.
2) 2x + 7y = 3
x = 1 - 4y
Similar to the previous problem, we'll substitute x from the second equation into the first equation:
2(1 - 4y) + 7y = 3
Distribute 2 to the terms inside the parentheses:
2 - 8y + 7y = 3
Combine like terms:
2 - y = 3
Now, solve for y:
-y = 3 - 2
-y = 1
y = -1
Substitute the value of y back into the second equation to find x:
x = 1 - 4(-1)
x = 1 + 4
x = 5
So, the solution to this system is x = 5 and y = -1.
3) x = 2y
4x + 2y = 15
In this case, we already have x isolated in the first equation, so we'll substitute x in terms of y into the second equation:
4(2y) + 2y = 15
Multiply and combine like terms:
8y + 2y = 15
10y = 15
Now, solve for y:
y = 15/10
y = 1.5
Substitute the value of y back into the first equation to find x:
x = 2(1.5)
x = 3
Thus, the solution to this system is x = 3 and y = 1.5.
Remember to always double-check your solutions by substituting them back into the original equations to verify if they satisfy both equations.
I hope this explanation helps you better understand the process of substitution. If you have any more questions, feel free to ask!