Question

solve the system using elimination

2x-3y=-1
3x+4y=7
shows all steps

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using elimination, we will multiply the first equation by 4 and the second equation by 3 to make the coefficient of y the same:

4(2x-3y)=-4(-1)
3(3x+4y)=3(7)

Simplifying, we get:

8x-12y=4
9x+12y=21

Now we eliminate the variable y by adding the two equations:

(8x-12y)+(9x+12y)=4+21

Combining like terms, we get:

17x=25

To solve for x, divide both sides of the equation by 17:

17x/17=25/17

Simplifying, we get:

x=25/17

Now we substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:

2(25/17)-3y=-1

Multiplying through by 17 to get rid of the fraction, we get:

50-51y=-17

Subtracting 50 from both sides, we get:

-51y=-67

Dividing by -51, we get:

y=(-67)/(-51)

Simplifying, we get:

y=67/51

Thus, the solution to the system of equations is:

x = 25/17
y = 67/51

Answer 2

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

To solve the system of equations using elimination, we will eliminate one variable by multiplying one or both of the equations by a specific number and then adding or subtracting the equations. Here are the steps:

Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:
(3)(2x - 3y) = (3)(-1)
(2)(3x + 4y) = (2)(7)

Simplifying the equations, we get:
6x - 9y = -3
6x + 8y = 14

Step 2: Now, subtract the first equation from the second equation to eliminate x:
(6x + 8y) - (6x - 9y) = 14 - (-3)

Simplifying the equation, we get:
6x - 6x + 8y + 9y = 14 + 3
17y = 17

Step 3: Divide both sides of the equation by 17 to solve for y:
y = 1

Step 4: Substitute the value of y into either equation to solve for x. Let's substitute it into the first equation:
2x - 3(1) = -1
2x - 3 = -1

Step 5: Add 3 to both sides of the equation:
2x = 2

Step 6: Divide both sides of the equation by 2 to solve for x:
x = 1

So, the solution to the system of equations is x = 1 and y = 1.

Answer 3

[AI-generated answer — Explain Bot]

To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the two equations. Here are the steps to solve this system:

Step 1: Multiply one or both equations by appropriate constants to make the coefficients of one of the variables the same value. In this case, we can multiply the first equation by 4 and the second equation by 3 to make the coefficients of 'y' the same:

Equation 1: 4(2x - 3y) = 4(-1) -> 8x - 12y = -4
Equation 2: 3(3x + 4y) = 3(7) -> 9x + 12y = 21

Step 2: Add the new equations together to eliminate 'y'.

(8x - 12y) + (9x + 12y) = -4 + 21
17x = 17
x = 1

Step 3: Substitute the found value 'x' back into one of the original equations to solve for 'y'. Let's use the first equation:

2(1) - 3y = -1
2 - 3y = -1
-3y = -3
y = 1

Therefore, the solution of the system is x = 1, y = 1.