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