3x+5y=4 and 2x+7y=3
I need to figure the solution using the substitution
method of systems of linear equations
The substitution method starts by solving one of the
equations for x in terms of y, or y in terms of x. Then,
you substitute that value into the other equation for
whichever variable you found from the first equation.
3x+5y=4
5y = -3x + 4
y = (-3/5)x + 4/5
Substitute that into the second equation.
2x+7y=3
2x + 7 * ((-3/5)x + 4/5) = 3
2x + ((-21/5)x + 28/5) = 3
2x - (21/5)x + 28/5 = 3
2x - (21/5)x = 3 - (28/5)
Change those whole numbers into fractions with
the common denominator, 5.
(10/5)x - (21/5)x = (15/5) - (28/5)
(-11/5)x = (-13/5)
Now, multiply both sides by (-5/11).
(-11/5)x * (-5/11) = (-13/5) * (-5/11)
x = 13/11
To find y, substitute the value of x into the first equation.
3(13/11) + 5y = 4
(39/11) + 5y = 4
5y = 4 - (39/11)
Multiply through by 11.
5y * 11 = (4 * 11) - (39/11) * 11
55y = 44 - 39
55y = 5
y = 5/55
y = 1/11
There you have it: x = 13/11, and y = 1/11