How do you solve the following system of equations by linear combination: 3x+2y=-7, 5x-4y=19?

Oct 4, 2017

Solution: $x = \frac{4}{11} , y = - \frac{46}{11}$

Explanation:

$3 x + 2 y = - 7 \left(1\right) , 5 x - 4 y = 19 \left(2\right)$ . Multiplying equation (1) by $2$

we get $6 x + 4 y = - 14 \left(3\right)$ Adding equation (2) and equation (3)

we get $11 x = 5 \mathmr{and} x = \frac{5}{11}$ . Putting $x = \frac{5}{11}$ in equation (1) we

get $3 \cdot \frac{5}{11} + 2 y = - 7 \mathmr{and} 2 y = - 7 - \frac{15}{11} \mathmr{and} 2 y = - \frac{92}{11}$

or $y = - \frac{92}{22} \mathmr{and} y = - \frac{46}{11} \mathmr{and}$

Solution: $x = \frac{4}{11} , y = - \frac{46}{11}$ [Ans]