Question

I need help with substitution! Find the solution.

Here are the two equations:
5x - 6y =19
4x + 3y = 10

Answer 1

5x - 6y = 19 ------------- (1)
4x + 3y = 10 -------------(2)

From (2):
4x + 3y = 10
3y = 10 - 4x
6y = 20 - 8x -------- sub into (1)

5x - (20 - 8x) = 19
5x - 20 + 8x = 19
13x - 20 = 19
13x = 19 + 20
13x = 39
x = 3 ---- sub into (1)
5 (3) - 6y = 19
-6y = 19 - 15
-6y = 4
y = - 2/3

Ans: x = 3, y = -2/3

Answer 2

Solve the following system using substitution:
{5 x - 6 y = 19
{4 x + 3 y = 10

In the first equation, look to solve for x:
{5 x - 6 y = 19
{4 x + 3 y = 10

Add 6 y to both sides:
{5 x = 6 y + 19
{4 x + 3 y = 10

Divide both sides by 5:
{x = (6 y)/5 + 19/5
{4 x + 3 y = 10

Substitute x = (6 y)/5 + 19/5 into the second equation:
{x = (6 y)/5 + 19/5
{3 y + 4 ((6 y)/5 + 19/5) = 10

3 y + 4 ((6 y)/5 + 19/5) = ((24 y)/5 + 76/5) + 3 y = (39 y)/5 + 76/5:
{x = (6 y)/5 + 19/5
{(39 y)/5 + 76/5 = 10

In the second equation, look to solve for y:
{x = (6 y)/5 + 19/5
{(39 y)/5 + 76/5 = 10

Subtract 76/5 from both sides:
{x = (6 y)/5 + 19/5
{(39 y)/5 = -26/5

Multiply both sides by 5/39:
{x = (6 y)/5 + 19/5
{y = -2/3


Substitute y = -2/3 into the first equation:

Answer: {x = 3, y = -2/3