Determine the x-coordinate of the solution of the system of equations below. You may use any method:
2x-y=10
x+y=2
Determine the y-coordinate of the solution for the system of equations. You may use any method.
2x-y=10
x+y=2
Plz help i really don't understand these two Q please help by showing me step by step ;-; im so sorry
these two make substitution the method of choice.
x+y=2 means y = 2-x
So, using that in the other equation,
2x-(2-x) = 10
2x-2+x = 10
3x = 12
x = 4
now use either equation to see that y = -2
check:
2*4-(-2) = 8+2 = 10
4+(-2) = 4-2 = 2
similarly, you can substitute for x:
x = 2-y
2(2-y)-y=10
4-2y-y=10
-3y=6
y = -2
2*
No problem! I can help you with that. To solve this system of equations, we can use the method of substitution or the method of elimination. I will show you both methods step by step.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y:
x + y = 2
y = 2 - x
Step 2: Substitute the expression found in step 1 into the other equation.
Substitute y = 2 - x into the first equation:
2x - (2 - x) = 10
Step 3: Simplify and solve for x.
2x - 2 + x = 10
3x - 2 = 10
3x = 12
x = 4
Step 4: Substitute the value of x back into one of the original equations to find y.
Using the second equation:
x + y = 2
4 + y = 2
y = 2 - 4
y = -2
So the solution to the system of equations is x = 4 and y = -2.
Method 2: Elimination
Step 1: Multiply one or both equations by a constant such that the coefficient of one variable in one equation is the same as the coefficient of that variable in the other equation. Let's multiply the second equation by 2 to make the coefficients of y in both equations equal:
2(x + y) = 2(2)
2x + 2y = 4
Step 2: Add the equations together to eliminate one variable.
(2x - y) + (2x + 2y) = 10 + 4
4x + y = 14
Step 3: Solve the resulting equation for one variable.
y = 14 - 4x
Step 4: Substitute the value found in step 3 into one of the original equations.
Substitute y = 14 - 4x into the first equation:
2x - (14 - 4x) = 10
Step 5: Simplify and solve for x.
2x - 14 + 4x = 10
6x - 14 = 10
6x = 24
x = 4
Step 6: Substitute the value of x back into one of the original equations to find y.
Using the second equation:
x + y = 2
4 + y = 2
y = 2 - 4
y = -2
So the solution to the system of equations is x = 4 and y = -2.
I hope this helps! Let me know if you have any further questions.
Don't worry, I'm here to help you with these questions step by step.
For the first question, we need to determine the x-coordinate of the solution for the given system of equations:
1. We have the equations:
2x - y = 10 ----(1)
x + y = 2 ----(2)
2. There are several methods you can use to solve this system, such as substitution, elimination, or graphing. Let's use the method of elimination:
3. To eliminate one variable, add the two equations together:
(2x - y) + (x + y) = 10 + 2
Simplify the equation:
3x = 12
4. Now, solve for x by dividing both sides of the equation by 3:
3x/3 = 12/3
x = 4
5. So the x-coordinate of the solution is x = 4.
For the second question, we need to determine the y-coordinate of the solution for the given system of equations:
1. We have the equations:
2x - y = 10 ----(1)
x + y = 2 ----(2)
2. We can use the same method of elimination to find the y-coordinate:
3. Add the two equations together:
(2x - y) + (x + y) = 10 + 2
Simplify the equation:
3x = 12
4. Now, solve for x using the same steps as before:
3x/3 = 12/3
x = 4
5. Substitute the value of x into either of the original equations to solve for y. Let's use equation (2):
x + y = 2
4 + y = 2
Simplify the equation:
y = 2 - 4
y = -2
6. So the y-coordinate of the solution is y = -2.
I hope this helps you understand how to solve these types of questions step by step. Let me know if you have any further questions!