## I need help with substitution! Find the solution. Here are the two equations: 5x – 6y =19 4x + 3y = 10

Question

I need help with substitution! Find the solution.
Here are the two equations:
5x – 6y =19
4x + 3y = 10

0

1. 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

2. 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