How would you solve these systems? I need help
1. X=3
2x-4y=5
2. X=3
4y=2x+18
3. Y=3
4y=2x+18
1. Plug x = 3 into the equation 2x - 4y = 5 and solve.
Do the same for 2 and 3.
It's substitution
I know it is but how would you do that's what I'm asking.
If you know that x = 3 for example
Then use 3 instead of x in the next equation
and all will be well.
To solve a system of equations, you can use either the substitution method or the elimination method. I'll explain both methods for each system of equations you provided.
1. X = 3
2x - 4y = 5
Substitution Method:
Since we already have the value of X, which is 3, we can substitute it directly into the second equation.
2(3) - 4y = 5
6 - 4y = 5
-4y = 5 - 6
-4y = -1
Divide both sides of the equation by -4:
y = -1/-4
y = 1/4
So the solution to this system is X = 3 and y = 1/4.
Elimination Method:
Multiply the first equation by 2 to make the coefficients of X the same in both equations:
2(X) = 2(3)
2x = 6
Now, we can subtract the modified first equation from the second equation:
(2x - 4y) - (2x) = 5 - 6
-4y = -1
Divide both sides by -4:
y = 1/4
Again, we obtain the solution X = 3 and y = 1/4.
2. X = 3
4y = 2x + 18
For this system, we already have the value of X, so we can substitute it directly into the second equation:
4y = 2(3) + 18
4y = 6 + 18
4y = 24
Divide both sides by 4:
y = 24/4
y = 6
Therefore, the solution to this system is X = 3 and y = 6.
3. Y = 3
4y = 2x + 18
Substitution Method:
Since we already have the value of y, which is 3, we can substitute it directly into the second equation:
4(3) = 2x + 18
12 = 2x + 18
Subtract 18 from both sides of the equation:
2x = 12 - 18
2x = -6
Divide both sides by 2:
x = -6/2
x = -3
So the solution to this system is x = -3 and y = 3.
Elimination Method:
Multiply the first equation by 2 to make the coefficients of y the same in both equations:
2(Y) = 2(3)
2y = 6
Now, we can subtract the modified first equation from the second equation:
(4y) - (2y) = (2x + 18) - 6
2y = 2x + 12
Divide both sides by 2:
y = (2x + 12)/2
y = x + 6
Since we know y = 3, we can substitute it into the equation:
3 = x + 6
Subtract 6 from both sides:
x = 3 - 6
x = -3
So the solution to this system is x = -3 and y = 3.
I hope that helps! Let me know if you have any other questions.