solve the system using substitution
{x+2y=11
{3x+2y=13
i just told you how to do the other one; it's the same exact method. solve for x and y. you get: x=-2y+11 and y=(-1/2x)+(11/2). then plug them both back into the original equation (either one, it doesn't matter); you get, x=11, and y=0. the points would be (11,0)
thats not one of the options on the multiple choice though....
they are....
a-(1,5)
b-(16,-2.6)
c-(-1,6)
d-(12,-0.5)
I'm so sorry, I put 11 where I should have put 13. The answer is A) 1,5. That's right. Sorry again.
Well, I must say, that was quite a twist! It seems I made a slight error there. Thank you for catching that. But hey, at least I provided a good opportunity for a laugh, right? Don't worry, mistakes happen to the best of us. Keep up the great work!
No problem at all! We all make mistakes. Just to clarify, let's solve the system step-by-step using substitution.
Given the system of equations:
1) x + 2y = 11
2) 3x + 2y = 13
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve equation 1) for x:
x = 11 - 2y
Step 2: Substitute the expression for x from step 1) into the other equation (equation 2). We have:
3(11 - 2y) + 2y = 13
Step 3: Simplify and solve for y:
33 - 6y + 2y = 13
-4y = 13 - 33
-4y = -20
y = (-20)/(-4)
y = 5
Step 4: Substitute the value of y back into equation 1) to solve for x:
x + 2(5) = 11
x + 10 = 11
x = 11 - 10
x = 1
Therefore, the solution to the system of equations {x + 2y = 11, 3x + 2y = 13} is x = 1 and y = 5. The correct answer is A) (1,5).
I apologize for the earlier confusion and any inconvenience caused.
To solve the system of equations using the substitution method, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, x + 2y = 11, for x:
x = 11 - 2y
2. Substitute the expression for x obtained in step 1 into the other equation.
Substitute x = 11 - 2y into the second equation, 3x + 2y = 13:
3(11 - 2y) + 2y = 13
3. Simplify and solve the resulting equation for the remaining variable.
Distribute 3 to the terms inside the parentheses:
33 - 6y + 2y = 13
Combine like terms:
-4y + 33 = 13
Subtract 33 from both sides of the equation:
-4y = -20
Divide both sides by -4:
y = 5
4. Substitute the value of y back into one of the original equations to solve for x.
Using the first equation, x + 2y = 11:
x + 2(5) = 11
x + 10 = 11
Subtract 10 from both sides of the equation:
x = 1
So the solution to the system of equations is x = 1 and y = 5. Therefore, the correct answer is A) (1,5). I apologize for the previous incorrect response.