0.3x-0.2y=4 0.4x+0.3y=49/23
solve by elimination method
We can make it easier on ourselves by
getting rid of the decimals. Multiply through
by 10
10 * (0.3x-0.2y) = 10 * 4
3x - 2y = 40
Also,
10 * (0.4x+0.3y) = 10 * (49/23)
4x + 3y = 490/23
To eliminate the y terms, the coefficients
must be the same. (At least the absolute
value has to be the same.)
Let's make them 6.
3 * (3x - 2y) = 3 * 40
9x - 6y = 120
and
2 * (4x + 3y) = 2 * (490/23)
8x + 6y = 980/23
We can now add the two equations,
thus eliminating the y term.
9x - 6y = 120
+(8x + 6y = 980/23)
------------------------------
17x = 120 + 980/23
120 is 2760/23
17x = 2760/23 + 980/23 = 3740/23
Divide through by 17.
x = 220/23
Solve for y
0.4(220/23) + 0.3y = 49/23
88/23 + 0.3y = 49/23
0.3y = 48/23 - 88/3 = -39/23
y = (-39/23) / 0.3 = (-39/23) / (3/10)
y = (-39/23) * (10/3) = (-39 * 10) / (23 * 3)
y = (-390) / (23 * 3) = -130 / 23
Put those into the first equation.
0.3(220/23) - 0.2(-130 / 23) = 4
66/23 + 26/23 = 92/23 = 4
x = 220/23 and y = -130/23