Question

solve.

y=-1/2x+6
y=3x - 1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can set the two equations equal to each other since they both equal y:

-1/2x + 6 = 3x - 1

Next, let's simplify the equation:

-1/2x - 3x = -1 - 6

-7/2x = -7

Next, let's solve for x by multiplying both sides of the equation by 2/7:

x = (-7)(2/7)

x = -2

Now, substitute the value of x back into one of the original equations to solve for y:

y = 3(-2) - 1

y = -6 - 1

y = -7

Therefore, the solution to the system of equations is x = -2 and y = -7.

Answer 2

[AI-generated answer — Step-by-Step Bot]

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

Step 1:

We have two equations:
1) y = -1/2x + 6
2) y = 3x - 1

Since both equations are equal to y, we can set them equal to each other:

-1/2x + 6 = 3x - 1

Step 2:

To get rid of the fractions, let's multiply every term in the equation by 2:

-2(1/2x) + 2(6) = 2(3x) - 2(1)

Simplifying:

-x + 12 = 6x - 2

Step 3:

Let's solve for x by adding x to both sides and subtracting 12 from both sides:

-x + x + 12 = 6x + x - 2 + 12

Simplifying:

12 = 7x + 10

Step 4:

Next, subtract 10 from both sides:

12 - 10 = 7x + 10 - 10

Simplifying:

2 = 7x

Step 5:

Finally, divide both sides by 7 to solve for x:

2/7 = 7x/7

Simplifying:

x = 2/7

Step 6:

To find the value of y, substitute the value of x back into one of the original equations. Let's use the second equation:

y = 3(2/7) - 1

Simplifying:

y = 6/7 - 1

Step 7:

To subtract fractions, we need to have a common denominator. In this case, it is 7. So let's write 1 as 7/7:

y = 6/7 - 7/7

Simplifying:

y = -1/7

Step 8:

Therefore, the solution to the system of equations is x = 2/7 and y = -1/7.

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations y = -1/2x + 6 and y = 3x - 1, we can use the method of substitution. Here's how:

Step 1: Set the two equations equal to each other:
-1/2x + 6 = 3x - 1

Step 2: Simplify and bring all x terms to one side and all constant terms to the other side:
-1/2x - 3x = -1 - 6
-4.5x = -7

Step 3: Divide both sides of the equation by -4.5 to solve for x:
x = -7 / -4.5
x = 1.56 (rounded to two decimal places)

Step 4: Substitute the value of x back into either equation to find the value of y. Let's use the first equation:
y = -1/2(1.56) + 6
y = -0.78 + 6
y = 5.22

Step 5: Therefore, the solution to the system of equations is x = 1.56 and y = 5.22.