x+y=5
x-y=3
Please help me solve this system of equation and show your work thanks
just add them as they are ...
2x = 8
x = 4
back into the 1st:
x+y=5
4+y=5
y = 1
x=4, y=1
you can also use the process of elimination so : 2x=8 when u add them, x=4 and plug it in to whatever equation.
come on, that's too easy!
To solve this system of equations, you can use either the substitution method or the elimination method. I will demonstrate the elimination method here:
First, let's write the system of equations again:
Equation 1: x+y=5
Equation 2: x-y=3
To eliminate one variable, we can add Equation 1 and Equation 2 together. When we add the left sides and the right sides, we get:
(x + y) + (x - y) = 5 + 3
Simplifying both sides of the equation, we have:
2x = 8
To isolate x, we divide both sides of the equation by 2:
2x/2 = 8/2
x = 4
Now that we have found the value of x, we can substitute it into one of the original equations to solve for y. Let's use Equation 1:
x + y = 5
Substituting x = 4 into the equation, we have:
4 + y = 5
To isolate y, we subtract 4 from both sides of the equation:
4 + y - 4 = 5 - 4
y = 1
Therefore, the solution to the system of equations is x = 4 and y = 1.
To solve the system of equations, we can use the method of elimination or substitution. I will demonstrate both methods so you can choose the one you find more convenient.
Method 1: Elimination
1. Start with the two equations:
x + y = 5 -- (Equation 1)
x - y = 3 -- (Equation 2)
2. Add Equation 1 and Equation 2 together:
(x + y) + (x - y) = 5 + 3
Simplifying the equation leads to:
2x = 8
3. Divide both sides of the equation by 2 to isolate x:
2x / 2 = 8 / 2
Which gives us:
x = 4
4. Now that we have the value of x, we can substitute it back into one of the original equations to find y. Let's use Equation 1:
4 + y = 5
Subtracting 4 from both sides of the equation, we get:
y = 1
5. Therefore, the solution for the system of equations is x = 4 and y = 1.
Method 2: Substitution
1. Start with the two equations:
x + y = 5 -- (Equation 1)
x - y = 3 -- (Equation 2)
2. Solve Equation 2 for x:
x = y + 3
3. Substitute the value of x from Equation 2 into Equation 1:
(y + 3) + y = 5
Simplifying the equation, we get:
2y + 3 = 5
4. Subtract 3 from both sides of the equation to isolate 2y:
2y = 5 - 3
Which gives us:
2y = 2
5. Divide both sides of the equation by 2 to solve for y:
2y / 2 = 2 / 2
Which gives us:
y = 1
6. Now that we have the value of y, substitute it back into Equation 2 to find x:
x - 1 = 3
Adding 1 to both sides of the equation, we get:
x = 4
7. Therefore, the solution for the system of equations is x = 4 and y = 1.
Both methods yield the same solution, which is x = 4 and y = 1. You can check the solution by substituting these values back into the original equations to verify that they hold true.