Answer:
Step-by-step explanation:
To solve the system of equations:
3
⋅
1
0
−
5
=
17
3⋅10
−5
r=17
9
+
2
=
−
17
9e+2r=−17
Let's proceed step by step:
Step 1: Solve the first equation for
r
3
⋅
1
0
−
5
=
17
3⋅10
−5
r=17
Divide both sides by
3
⋅
1
0
−
5
3⋅10
−5
:
=
17
3
⋅
1
0
−
5
r=
3⋅10
−5
17
To simplify
17
3
⋅
1
0
−
5
3⋅10
−5
17
:
=
17
3
⋅
1
0
5
r=
3
17
⋅10
5
=
17
3
⋅
100000
r=
3
17
⋅100000
=
1700000
3
r=
3
1700000
=
566666.67
r=566666.67
So,
≈
566666.67
r≈566666.67.
Step 2: Substitute
r into the second equation to find
e
Now substitute
=
566666.67
r=566666.67 into the second equation:
9
+
2
=
−
17
9e+2r=−17
9
+
2
⋅
566666.67
=
−
17
9e+2⋅566666.67=−17
9
+
1133333.34
=
−
17
9e+1133333.34=−17
Subtract 1133333.34 from both sides:
9
=
−
17
−
1133333.34
9e=−17−1133333.34
9
=
−
1133350.34
9e=−1133350.34
Divide both sides by 9:
=
−
1133350.34
9
e=
9
−1133350.34
=
−
125927.8156
e=−125927.8156
So,
≈
−
125927.82
e≈−125927.82.
Conclusion:
The solutions to the system of equations are approximately:
≈
566666.67
r≈566666.67
≈
−
125927.82
e≈−125927.82
