# O solve this system of equations by addition, what could you multiply each equation by to cancel out the x-variable? A: 5x - 2y = 10 B: 4x + 3y = 7

Mar 27, 2016

Multiply $5 x - 2 y = 10$ by $4$.
Multiply $4 x + 3 y = 7$ by $5$.

#### Explanation:

In order to cancel out the $x$ variable, the coefficient of $x$ in both equations must be equal. Thus, find the L.C.M. (lowest common multiple) of $4$ and $5$, which is $20$.

For $5 x - 2 y = 10$, in order to make the coefficient of $5 x$ be $20$, the whole equation must be multiplied by $4$.

$4 \left(5 x - 2 y = 10\right)$

$\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{\text{Equation} \textcolor{w h i t e}{i} 1}$: $20 x - 8 y = 40$

Similarly, for $4 x + 3 y = 7$, in order to make the coefficient of $4 x$ be $20$, the whole equation must be multiplied by $5$.

$5 \left(4 x + 3 y = 7\right)$

color(darkorange)("Equation"color(white)(i)2: $20 x + 15 y = 35$

Since elimination works by subtracting one equation from the other, if you try subtracting equation $2$ from equation $1$, the terms with $x$ will become $\textcolor{b l u e}{\text{zero}}$.

$\textcolor{w h i t e}{X x} 20 x - 8 y = 40$
$\frac{- \left(20 x + 15 y = 35\right)}{\textcolor{b l u e}{0 x} - 23 y = 5}$