Choose the ordered pair that is a solution to the system of equations.
3x - y = 10
-x + y = -4
(3, -7)
(-1, 3)
(3, -1)
(3, 1)
Follow the example I gave in your previous question. I'm not going to do all of them.
You want to eliminate one of the variable and solve. Then substitute into an equation and sovle for the other variable.
If you add the equations together
3x - y = 10
-x + y = -4
you get
2x = 6
Solve for x and substitute into either equation to solve for the other variable.
x = 3
Substitute into the first equation
3(3) - y = 10
9 - y = 10
y = -1
So the ordered pair is (3, -1).
To find the solution to the system of equations, let's follow the steps you mentioned:
Step 1: Eliminate one of the variables by adding the equations together.
The system of equations is:
3x - y = 10
-x + y = -4
If we add the two equations together, we get:
(3x - y) + (-x + y) = 10 + (-4)
3x - y - x + y = 6
2x = 6
Step 2: Solve for x.
To isolate the variable x, divide both sides of the equation by 2:
2x/2 = 6/2
x = 3
Step 3: Substitute x = 3 into one of the equations to solve for the other variable.
Let's substitute x = 3 into the first equation:
3x - y = 10
3(3) - y = 10
9 - y = 10
Step 4: Solve for y.
To isolate the variable y, subtract 9 from both sides of the equation:
- y = 10 - 9
- y = 1
Step 5: Determine the ordered pair solution.
Now that we have found the values of x and y, we can write them as an ordered pair.
The solution to the system of equations is (x, y) = (3, 1).
Out of the given answer choices:
(3, -7): This does not satisfy either equation in the system.
(-1, 3): This does not satisfy either equation in the system.
(3, -1): This does not satisfy the second equation (-x + y = -4).
(3, 1): This satisfies both equations in the system and is the correct solution.
Therefore, the ordered pair that is a solution to the system of equations is (3, 1).
To solve the system of equations:
3x - y = 10
-x + y = -4
First, let's eliminate one of the variables. Adding the two equations together will eliminate the y variable:
(3x - y) + (-x + y) = 10 + (-4)
Simplifying, we get:
2x = 6
Now, let's solve for x. Dividing both sides of the equation by 2 gives us:
x = 3
Next, we substitute the value of x into one of the original equations to solve for the other variable. Let's use the second equation:
-x + y = -4
Substituting x = 3 into this equation, we have:
-3 + y = -4
Simplifying, we get:
y = -4 + 3
y = -1
Therefore, the ordered pair that is a solution to the system of equations is (3, -1).