solve the system by substitution
solve the system by substitution
x=4y-11
-3x+4z=-7
y=-5x+2z+25
almost made it but got stuck at the end.
1) x = 4y - 11
2) -3x + 4z = -7
3) y = -5x + 2z + 25
Equation 3 already has y in terms of x, so substitute
that for y in equation 1.
x = 4y - 11
x = 4(-5x + 2z + 25) - 11
x = -20x + 8z + 100 - 11
x + 20x - 8z = -20x + 8z + 89 + 20x - 8z
4) 21x - 8z = 89
Now, there are two equations with x and z.
Solve equation 2 for x and substitute that into
equation 4.
-3x + 4z = -7
-3x + 4z - 4z = -7 - 4z
-3x = -7 - 4z
x / -3 = -7/-3 - (4/-3)z
x = 7/3 + 4/3z
21x - 8z = 89
21(7/3 + 4/3z) - 8z = 89
49 + 28z -8z = 89
49 + 20z - 49 = 89 - 49
20z = 40
20z / 20 = 40 / 20
z = 2 <<<<<<<<<<<<<<<<<<
Plug that into equation 2 and solve for x.
-3x + 4z = -7
-3x + 4(2) = -7
-3x + 8 = -7
-3x + 8 - 8 = -7 - 8
-3x = -15
-3x / -3 = -15 / -3
x = 5 <<<<<<<<<<<<<<<<<<
Plug the value of x into equation 1 and solve for y.
x = 4y - 11
5 = 4y - 11
5 + 11 = 4y - 11 + 11
16 = 4y
4y = 16
4y / 4 = 16 / 4
y = 4 <<<<<<<<<<<<<<<<<<
Use all three of the original equations to check your answers.
1) x = 4y - 11
5 = 4(4) - 11
5 = 16 - 11
5 = 5
2) -3x + 4z = -7
-3(5) + 4(2) = -7
-15 + 8 = -7
-7 = -7
3) y = -5x + 2z + 25
4 = -5(5) + 2(2) + 25
4 = -25 + 4 + 25
4 = 4
Answer: x = 5, y = 4, z = 2