What is the \(x\)-coordinate of the intersection point \((x,y)\) of the system below? $$ 3.2x-1.5y=0.3$$ $$ 0.6x+0.5y=-5.1$$

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To obtain the \(x\)-coordinate, eliminate \(y\).

$$ 3.2x-1.5y=0.3$$

Multiplying each term of the second equation by 3,

$$ 3(0.6x+0.5y)=-5.1(3)$$ $$ 1.8x+1.5y=-15.3$$

Adding each term,

$$ \begin{array}{ c c c} &3.2x & -1.5y & 0.3 \\ +&1.8x & 1.5y & -15.3 \\ \hline \end{array} $$ $$ 5x = -15 $$ $$ x= \boxed{-3}$$

Multiplying each term of both equations by 10 would get rid of the decimals, if you'd prefer to avoid them.

$$ 10(3.2x-1.5y)=0.3(10)$$ $$ 32x-15y=3$$ $$ 10(0.6x+0.5y)=-5.1(10)$$ $$6x+5y=-51$$

We can choose to use elimination or substitution from here on.