use substitution to solve the linear system

3x+2y=-5
4x-3y=16

help plz!!!

Solve for y in one formula, and then substitute that value for y in the other formula to solve for x. Once you find x, substitute that value into either formula to get the value for y.

-3y = 16 - 4x

y = (16 - 4x)/-3 = (4/3)x - 16/3

I'll let you do the rest.

I hope this helps. Thanks for asking.

Now we substitute y in the first equation:

3x + 2((4/3)x - 16/3) = -5
3x + (8/3)x - 32/3 = -5

Now, we find a common denominator to combine the fractions:

(9/3)x + (8/3)x = (-5 + 32/3)
(17/3)x = 7/3

Now, we can find the value of x by dividing both sides by 17/3

(17/3)x / (17/3) = 7/3 / (17/3)
x = 7/17

Now, substitute x back into the equation we found for y:

y = (4/3)(7/17) - 16/3
y = 28/51 - 16/3
y = 28/51 - 272/51
y = -244/51

So the solution of the linear system is x = 7/17 and y = -244/51.

To solve the linear system using substitution, we can start by isolating one variable in one of the equations and then substitute that expression into the other equation.

Let's start with the first equation:

3x + 2y = -5 ... (equation 1)

We can isolate y by subtracting 3x from both sides:

2y = -5 - 3x

Now, divide both sides of the equation by 2 to solve for y:

y = (-5 - 3x) / 2 ... (equation 2)

Now that we have the expression for y in terms of x, we can substitute this expression into the second equation:

4x - 3y = 16

Replacing y with (-5 - 3x) / 2:

4x - 3((-5 - 3x) / 2) = 16

Now, simplify the equation by distributing the 3 to both terms inside the parentheses:

4x - (3(-5) + 3(3x)) / 2 = 16

Simplify further:

4x - (-15 - 9x) / 2 = 16

To get rid of the fraction, we can multiply both sides of the equation by 2:

2(4x - (-15 - 9x)) = 2 * 16

Simplify the equation:

8x + 15 + 18x = 32

Combine like terms:

26x + 15 = 32

Now subtract 15 from both sides:

26x + 15 - 15 = 32 - 15

Simplify:

26x = 17

Finally, divide both sides by 26 to solve for x:

x = 17 / 26

Now that you have the value of x, you can substitute it back into equation 2 to solve for y.