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

Question

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## Answers ( No )

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

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