Question

Solving a System of Equations Using Linear Combination What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12

Answer 1

To eliminate the x term: We'll multiply the first equation by $3$ and the second equation by $-4$. Hence:

$\left \{ 3\times(4x + 5y) = 3\times7 \atop (-4)\times(3x-2y) = (-4)\times(-12)} \right\iff \left \{ 12x+15y=21 \atop -12x+8y=48 \right.$

Adding them, we'll obtain:

$0x+23y=69\iff y=\dfrac{69}{23}\iff \boxed{y=3}$

Substituting the value obtained in the first equation:

$4x + 5y = 7\Longrightarrow 4x+5\cdot3=7\iff 4x+15=7\iff 4x=-8\iff\\\\x=\dfrac{-8}{4}\iff \boxed{x=-2}$