# How do you solve for x and y in the equation 4x+2y=98?

May 5, 2015

I don't know the formal way of doing this, but here's the way I would do it.

$4 x + 2 y = 98$

$\implies 2 x + y = 49$

Now you know that

$2 - 1 = 1$

$\implies 2 \left(1\right) + 1 \left(- 1\right) = 1$

Multiplying both sides by $49$ you have,

$2 \left(49\right) + 1 \left(- 49\right) = 49$

Now, multiply both sides by $2$,

$4 \left(49\right) + 2 \left(- 49\right) = 98$

Compare this the original equation $4 x + 2 y = 98$

You see that $x = 49$ and $y = - 49$

Alternatively,

By graphing that equation: $4 x + 2 y = 98$
You discover that they are infinitely many solutions for this.

Each point $\left(x , y\right)$ is a possible solution

graph{-2x+49 [-50, 50, -50, 75]}