Given the following linear equations:
3x - 4y = 10
2x - 4y = 6
we are asked to test if (x, y) satisfies the system of equation and find the value of y.
3x - 4y = 10 ------------------------ eqn I
2x - 4y = 6 ------------------------- eqn II
Using elimination method, lets subtract eqn II from eqn I
3x - 4y = 10
-
2x - 4y = 6
the 4y will cancel out because of the negative sign introduced.
x = 4
substitute x = 4 into eqn I
recall, eqn I is:
3x - 4y = 10
3(4) - 4y = 10
12 - 4y = 10
lets collect like terms.
12 - 10 = 4y
2 = 4y
4y = 2
divide both sides by 4
4y/4 = 2/4
y = 1/2
x = 4, y = 1/2 ---------------> (4, 1/2)
lets substitute the values of x and y into any of the above equations:
recall, eqn I is 3x - 4y = 10
3(4) - 4(1/2) = 10
12 - 2 = 10
10 = 10
That means the equation satisfies the system of equation.