Question

Which ordered pair is the solution for the system? 2x − 3y = −19 4x + 5y = 17

Answer 1

To find the solution for this system of equations, we can use either substitution or elimination method.

1. Multiply the first equation by 5 and the second equation by 3 to eliminate y:

10x - 15y = -95

12x + 15y = 51

2. Add the two equations to eliminate y:

22x = -44

3. Divide both sides by 22 to solve for x:

x = -2

4. Substitute x = -2 into one of the equations to solve for y. Let's use the first equation:

2(-2) - 3y = -19

-4 - 3y = -19

-3y = -15

y = 5

Therefore, the ordered pair (-2, 5) is the solution for the system of equations 2x − 3y = −19 and 4x + 5y = 17.

Answer 2

(−2,5)

Explanation:

If you want to find x and y in this system of equations:

2x − 3y = −19

4x + 5y = 17

You can use elimination to get rid of one variable. Here's how:

First, double the first equation so that x has the same coefficient in both equations.

4x − 6y = −38

4x + 5y = 17

Then, subtract the first equation from the second equation to cancel out x and get a new equation with only y .

(4x + 5y) − (4x − 6y) = 17 − (−38)

11y = 55

Next, divide both sides by 11 to find the value of y .

y = 5

Now, plug in y = 5 into any of the original equations and solve for x .

2x − 3(5) = −19

2x = −4

x = −2

Finally, check that (−2,5) is the correct solution by substituting x = −2 and y = 5 into both original equations.

2(−2) − 3(5) = −19

−19 = −19

4(−2) + 5(5) = 17

17 = 17

So, the answer is (−2,5).