Solve the following system of equations, using the substitution method: 4x - 5 = 3 / 8x + 15 y = -24
Solve the following system of equations, using the substitution method:
4x - 5y = 3
8x + 15y = - 24
1) 4x - 5y = 3
2) 8x + 15y = - 24
Solve equation 1 for x in terms of y.
4x - 5y = 3
4x = 5y + 3
x = 5/4 y + 3/4
Substitute that into equation 2, in place of x.
8x + 15y = - 24
8(5/4 y + 3/4) + 15y = - 24
Solve for y.
8(5/4 y + 3/4) + 15y = - 24
(10y + 6) + 15y = -24
25y + 6 = -24
25y = -30
y = -30/25
y = -6/5
Substitute that into equation 1, in place of y.
4x - 5y = 3
4x - 5(-6/5) = 3
4x + 6 = 3
4x = 3 - 6
4x = -3
x = -3/4
Check the values by using them to solve
the original equations.
1) 4x - 5y = 3
4(-3/4) - 5(-6/5) = 3
-3 + 6 = 3
3 = 3
2) 8x + 15y = - 24
8(-3/4) + 15(-6/5) = - 24
-6 - 18 = -24
-24 = -24
Answer: x = -3/4, y = -6/5