Elimination using addition and subtraction:
1.
x - y = 1
x + y = 3
2.
-x + y = 1
x + y = 11
3.
x + 4y = 11
x - 6y = 11
4.
-x + 3y = 6
x + 3y = 18
PLEASE HELP!!!!
I NEED HELP ASAP!!!!
Either add or subtract one equation from the other to eliminate x.
For example. ADD the two equations in Problem 1. This results in 2x = 4, which requires that x = 2. Use either equation to get y.
You can certainly do the others yourself.
Sure, I'll help you solve these systems of equations using the method of elimination using addition and subtraction. Here's how to do it:
1. For the first set of equations:
- Start by adding the two equations together:
(x - y) + (x + y) = 1 + 3
Simplify the equation:
2x = 4
- Divide both sides of the equation by 2 to solve for x:
2x/2 = 4/2
x = 2
- Substitute the value of x back into one of the original equations to find y:
x + y = 3
2 + y = 3
Solve for y:
y = 3 - 2
y = 1
Therefore, the solution to the first set of equations is x = 2 and y = 1.
2. For the second set of equations:
- Start by adding the two equations together:
(-x + y) + (x + y) = 1 + 11
Simplify the equation:
2y = 12
- Divide both sides of the equation by 2 to solve for y:
2y/2 = 12/2
y = 6
- Substitute the value of y back into one of the original equations to find x:
x + y = 11
x + 6 = 11
Solve for x:
x = 11 - 6
x = 5
Therefore, the solution to the second set of equations is x = 5 and y = 6.
3. For the third set of equations:
- Start by subtracting the second equation from the first equation to eliminate x:
(x + 4y) - (x - 6y) = 11 - 11
Simplify the equation:
x + 4y - x + 6y = 0
Combine like terms:
10y = 0
- Divide both sides of the equation by 10 to solve for y:
10y/10 = 0/10
y = 0
- Substitute the value of y back into one of the original equations to find x:
x + 4y = 11
x + 4(0) = 11
Solve for x:
x = 11
Therefore, the solution to the third set of equations is x = 11 and y = 0.
4. For the fourth set of equations:
- Start by adding the two equations together:
(-x + 3y) + (x + 3y) = 6 + 18
Simplify the equation:
6y = 24
- Divide both sides of the equation by 6 to solve for y:
6y/6 = 24/6
y = 4
- Substitute the value of y back into one of the original equations to find x:
-x + 3y = 6
-x + 3(4) = 6
Solve for x:
-x + 12 = 6
-x = 6 - 12
-x = -6
Divide both sides of the equation by -1 to solve for x:
x = -6/-1
x = 6
Therefore, the solution to the fourth set of equations is x = 6 and y = 4.
I hope this helps! Let me know if you have any further questions.