Question

subtract the equations.
3x+4y=17
-(3x+2y=3)

Answer 1

-6x=14

6x=20

6y=20

2y=14

Answer 2

When we subtract the second equation from the first equation, we cancel out the terms with "x" and are left with:

(3x + 4y) - (3x + 2y) = 17 - 3

Simplifying the equation, we get:

3x - 3x + 4y - 2y = 14

This further simplifies to:

2y = 14

Dividing both sides of the equation by 2, we find:

y = 7

Now, we can substitute this value of y back into one of the original equations to solve for x. Plugging y = 7 into the first equation:

3x + 4(7) = 17

3x + 28 = 17

Subtracting 28 from both sides:

3x = -11

Dividing both sides by 3, we find:

x = -11/3

Therefore, the solution to the system of equations is x = -11/3 and y = 7.

Answer 3

To subtract the equations, we need to change the signs of the second equation and then combine like terms. Let's perform the operations step by step:

-6x = 14

- (6x) = - (20)

Simplifying the equation, we get:

-6x - 6x = 14 - 20

-12x = -6

To solve for x, we divide both sides of the equation by -12:

x = -6 / -12

Simplifying further, we have:

x = 1/2

Now, let's subtract the third equation from the fourth equation:

6y = 20

- (2y) = -(14)

Simplifying the equation, we get:

6y - 2y = 20 - 14

4y = 6

To solve for y, we divide both sides of the equation by 4:

y = 6 / 4

Simplifying further, we have:

y = 3/2

Therefore, the solutions to the equations are x = 1/2 and y = 3/2.