Question

69 points!!!
A system of equations is shown:

4x = −3y + 17
3x − 4y = −6

What is the solution to this system of equations?
(−2, −3)
(3, 2)
(2, 3)
(−3, −2)

Answer 1

Answer:

(2, 3)

Step-by-step explanation:

Given:  4x = −3y + 17  and  3x − 4y = −6

4x = -3y + 17

∴ 4x + 3y = 17  ⇒ (1)

   3x − 4y = −6 ⇒ (2)

Multiplying eq.(1) by 4 and eq.(2) by 3

16x + 12y = 68

9x - 12y = -18

Add the last 2 equations, the y terms will be eliminated

16x + 9x = 68 - 18

25x = 50

∴ x = 50/25 = 2

By substitution with x at eq.(1)

4*2 + 3y = 17

8 + 3y = 17

3y = 17 - 8 = 9

∴ y = 9/3 = 3

So, x = 2 and y = 3

The solution to this system of equations is (2,3)

Also see the attached figure which represent the graphical solution for the given system of equations

Answer 2

Using substitution, it is found that the solution of the system of equations is: (2,3).

The equations are:

$4x = -3y + 17$

$3x - 4y = -6$

From the second equation:

$3x = 4y - 6$

$x = \frac{4y - 6}{3}$

Replacing in the first:

$4x = -3y + 17$

$4\left(\frac{4y - 6}{3}\right) = -3y + 17$

Multiplying everything by 3:

$4(4y - 6) = -9y + 51$

$16y - 24 = -9y + 51$

$25y = 75$

$y = \frac{75}{25}$

$y = 3$

Then:

$x = \frac{4(3) - 6}{3} = \frac{6}{3} = 2$

Then, the solution is (2,3).

You can learn more about system of equations at https://brainly.com/question/14183076