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
