Solve for x and y by cross multiplication method: x + y= a - b , ax – by= a² + b².
Answers
Hii..
I'm feeling little sleepy so I'm attaching an image please go through it..
1.Solve
x + y = a + b
ax - by = a� - b�
Eliminate y
Multiply the first equation thru by b
bx + by = ab + b�
ax - by = a� - b�
Now add them vertically:
bx + by = ab + b�
ax - by = a� - b�
��-���������-�����������
bx+ax = ab+a�
bx + ax = ab + a�
Factor out x on the left, factor out a on the right
x(b + a) = a(b + a)
Divide both sides by (a + b)
x(b + a) a(a + b)
���������� = ����������
(a + b) (a + b)
x(b + a) a(a + b)
���������� = ����������
(a + b) (a + b)
x = a
Now eliminate x
Multiply the first equation thru by -a
-ax - ay = -a� - ab
ax - by = a� - b�
Now add them vertically:
-ax - ay = -a� - ab
ax - by = a� - b�
��-���������-�����������
-ay-by = -ab-b�
Multiply thru by -1
ay + by = ab + b�
Factor out y on the left, factor out b on the right
y(a + b) = b(a + b)
Divide both sides by (a + b)
y(a + b) b(a + b)
���������� = ����������
(a + b) (a + b)
y(a + b) b(a + b)
���������� = ����������
(a + b) (a + b)
y = b
2.Solve graphically system of equation 2x-y=5; 4x-y=8
Plot some points for 2x - y = 5
x | y
------
1 | -3
2 | -1
3 | 1
4 | 3
Plot some points for 4x - y = 8
x | y
------
1 | -4
2 | 0
3 | 4.
Notice that the point where the two lines intersect looks like it is
exactly to the right of -2 on the y-axis. It also look like it is
directly below 1 1/2 on the x-axis. So I would guess that the coordinates
of that point where they cross is (1.5, -2) so the answers read from the
way the graph looks are x = 1.5, y = -2
