Question

solve the system of equation

-x+6y=13
4x-10y=-10

Answer 1

[AI-generated answer — Explain Bot]

To solve this system of equations, you can use either the substitution method or the elimination method. I will walk you through the elimination method step-by-step:

Step 1: Multiply the first equation by 4 and the second equation by -1, so that the coefficients of x in both equations will cancel each other out when added together.

-4x + 24y = 52 (equation 1 multiplied by 4)
-4x + 10y = 10 (equation 2 multiplied by -1)

Step 2: Add the two equations together, canceling out the x terms:
-4x + 24y + (-4x + 10y) = 52 + 10

Simplifying the equation:
14y = 62

Step 3: Divide both sides of the equation by 14 to solve for y:
y = 62/14
y = 4.42857 (rounded to 5 decimal places)

Step 4: Substitute the value of y (4.42857) into either of the original equations to find the value of x. Let's use the first equation:

-x + 6(4.42857) = 13

Simplify the equation:
-x + 26.571 = 13

Step 5: Subtract 26.571 from both sides to solve for x:
-x = 13 - 26.571
-x = -13.571

Step 6: Multiply both sides of the equation by -1 to isolate x:
x = -1(-13.571)
x = 13.571

Thus, the solution to the system of equations is x = 13.571 and y = 4.42857 (or approximately x = 13.571 and y = 4.429).

Answer 2

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of elimination or substitution.

Method 1: Elimination

1. Multiply the first equation by 4 to make the coefficients of x in both equations equal:

-4x + 24y = 52

2. Add the two equations together to eliminate x:

(-4x + 24y) + (4x - 10y) = 52 + (-10)

Simplifying the equation, we get:

14y = 42

3. Solve for y by dividing both sides of the equation by 14:

y = 3

4. Substitute the value of y back into either of the original equations to solve for x. Let's use the first equation:

-x + 6(3) = 13

Simplifying the equation, we get:

-x + 18 = 13

5. Solve for x by subtracting 18 from both sides of the equation:

-x = -5

Dividing both sides by -1, we find:
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 3.

Method 2: Substitution

1. Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:

x = 6y + 13

2. Substitute this expression for x in the second equation:

4(6y + 13) - 10y = -10

Simplifying the equation, we get:

24y + 52 - 10y = -10

Combine like terms:
14y + 52 = -10

3. Solve for y by subtracting 52 from both sides of the equation:

14y = -62

Dividing both sides by 14, we find:
y = -4.43 (rounded to two decimal places)

4. Substitute this value of y back into the expression for x:

x = 6(-4.43) + 13

Simplifying the equation, we get:

x = -26.58 + 13

Add the numbers:
x = -13.58 (rounded to two decimal places)

Therefore, the solution to the system of equations is x = -13.58 and y = -4.43.

Answer 3

r u sure???

Answer 4

[AI-generated answer — Bot GPT 3.5]

Apologies for any confusion in my previous response. Let's go through the solution again:

We have the system of equations:

1) -x + 6y = 13
2) 4x - 10y = -10

To solve this system, we can use the method of substitution:

Step 1: Solve equation 1 for x:

-x + 6y = 13
=> x = 6y + 13

Step 2: Substitute x = 6y + 13 into equation 2:

4x - 10y = -10
=> 4(6y + 13) - 10y = -10

Simplifying the equation:

24y + 52 - 10y = -10
=> 14y + 52 = -10
=> 14y = -62
=> y = -62/14
=> y = -31/7

Step 3: Substitute y = -31/7 into equation 1 to solve for x:

-x + 6(-31/7) = 13
=> -x - 186/7 = 13
=> -x = 13 + 186/7
=> -x = (91 + 186)/7
=> -x = 277/7
=> x = -277/7

Therefore, the solution to the system of equations is x = -277/7 and y = -31/7.