Answer:
x = -34/3, y = 1/3, and z = -35/3
Step-by-step explanation:
2х+5y-3z-=14 let's call this equation 1.
x-2y=-12 let's call this equation 2.
-x+Зу-2z =13 let's call this equation 3.
USING EQUATION 1 AND EQUATION 3.
2х+5y-3z-=14 (EQUATION 1)
-x+Зу-2z =13 (EQUATION 3)
LET'S GET RID OF z, BY MAKING THE COEFFICIENT OF z IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY EQUATION 1 BY 2 AND EQUATION 3 BY 3.
2х+5y-3z-=14 (EQUATION 1) * 2
-x+Зу-2z =13 (EQUATION 3) * 3
4х+10y-6z-=28 let's call this equation 4.
-3x+9у-6z =39 let's call this equation 5.
TO GET RID OF z, WE WILL HAVE TO SUBTRACT EQUATION 5 FROM EQUATION 4 PLEASE TAKE NOTE OF THE SIGNS (-) (+).
4х+10y-6z-=28 (EQUATION 4)
- (-3x+9у-6z =39) (EQUATION 5)
(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)
x + y + 0 = -11
x + y = -11 let's call this equation 6.
USING EQUATION 2 AND EQUATION 6, LET'S FIND x AND y.
x-2y=-12 (EQUATION 2)
x + y = -11 (EQUATION 6)
x has the same coefficient in both equations, which is 1. Let's get rid of x so we can find the value of y.
We will subtract equation 6 from equation 2. Take note of the signs.
x-2y=-12 (EQUATION 2)
- (x + y = -11) (EQUATION 6)
(x - x) + ((-2y) - (+y)) = ((-12) - (-11))
0 + -3y = -1
-3y = -1
Divide both sides by -3.
-3y/-3 = -1/-3
y = 1/3
LET'S SUBSTITUTE THE VALUE OF y INTO EQUATION 2 TO GET THE VALUE OF x.
x-2y=-12 (EQUATION 2)
x-2(1/3)=-12
x -2/3 = -12
Add 2/3 to both sides.
x -2/3 + (2/3) = -12 + (2/3)
x + 0 = -34/3
x = -34/3
LET'S SUBSTITUTE THE VALUES OF x and y INTO EQUATION 1 TO GET THE VALUE OF z.
2х+5y-3z-=14 (EQUATION 1)
2(-34/3)+5(1/3)-3z-=14
-68/3 + 5/3 - 3z = 14
-21 - 3z = 14
Add 21 to both sides.
-21 + (21) - 3z = 14 + (21)
0 - 3z = 35
-3z = 35
Divide both sides by -3.
-3z/-3 = 35/-3
z = -35/3 or
Therefore, x = -34/3, y = 1/3, and z = -35/3
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