Download Answer on Question #55770 - Math – Algebra

Answer on Question #55770 - Math – Algebra
1. Solve the following system of equations algebraically. Verify the solution either graphically or by
using matrices.
3x – y = 0
5x + 2y = 22
2. Solve the following system of equations algebraically. Verify the solution either graphically or by
using matrices.
8x -2y = 5
-12x +3y = 7
Solution:
3x – y = 0
5x + 2y = 22
It follows from the first equation that y = 3x
Substitute for y = 3x into the second equation.
y = 3x
5x + 2*3x = 22
y = 3x
5x + 6x = 22
y = 3x
11x = 22
y = 3x
x = 22/11
y = 3x
x =2
y = 3∙ 2
x =2
y =6
x =2
5x
+
9
2y
8
2
7
Y
x
3
=2
y=
0
6
5
4
3
1
2
3
X
Answer:
3x – y = 0
5x + 2y = 22
x=2
y=6
2. Express y from the first equation and plug into the second equation.
8x -2y = 5
-12x + 3y = 7
→
8x - 5 = 2y
12x + 7 = 3y
→
y = (8x – 5)/2
12x + 7 = 3y
→ y = (8x – 5)/2
12x + 7 = 3∙(8x – 5)/2
→ y = (8x – 5)/2
12x + 7 = 1.5∙(8x – 5)
We solve the second equation:
12x + 7 = 12x – 7.5
12x – 12x = - 7 – 7.5
0 = - 14.5
The last equality does not hold, hence the previous equation and the system of equations have no
solution.
20
10
Y 0
-10
x
-12
+
=
3y
8x
7
2
5
=
y
-20
-30
-6
-4
-2
0
2
4
X
Answer:
8x -2y = 5
-12x +3y = 7
the system of equations has no solution
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