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*(4x + 5y) = 3*7 \atop (-4)*(3x-2y) = (-4)*(-12)} \right\iff \left \{ 12x+15y=21 \atop -12x+8y=48 \right.`

Adding them, we'll obtain:


`0x+23y=69\iff y=(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=(-8)/(4)\iff \boxed{x=-2}`