# How do I use elimination to find the solution of the system of equations y=1/3x+7/3 and y=−5/4x+11/4?

Jul 9, 2015

You multiply each equation by the LCM of the denominators and then solve by elimination as usual.

#### Explanation:

(1) $y = \frac{1}{3} x + \frac{7}{3}$
(2) $y = - \frac{5}{4} x + \frac{11}{4}$

Step 1: Multiply each equation by the least common multiple (LCM) of the denominator.

Multiply Equation 1 by $3$ and Equation 2 by $4$.

(3) $3 y = x + 7$
(4) $4 y = - 5 x + 11$

Step 2: To solve by elimination, multiply Equation 3 by $5$.

(5) $15 y = 5 x + 35$
(4) $4 y = - 5 x + 11$

Step 3: Add the two equations.

$19 y = 46$

(6) $y = \frac{46}{19}$

Step 4: Substitute Equation 6 into Equation 3.

x+7 = 3y = 3×46/19 = 138/19

$x = \frac{138}{19} - 7 = \frac{138 - 133}{19} = \frac{5}{19}$

The solution is $x = \frac{5}{19}$, $y = \frac{46}{19}$

Check:

Substitute in Equation 1.

$y = \frac{1}{3} x + \frac{7}{3}$

46/19 = 1/3× 5/19 + 7/3 = 5/57 + 7/3 = 5/57 + 133/57 =138/57 =46/19

Substitute in Equation 2.

$y = - \frac{5}{4} x + \frac{11}{4}$

46/19 = -5/4× 5/19 + 11/4 = -25/76 + 11/4 = -25/76 + 209/76 = 184/76 = 46/19