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Solve the following simultaneous equations $3 x+y=13$ $5 x-2 y=7$
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\begin{aligned} &3 x+y=13 \\ &5 x-2 y=7 \end{aligned}
The coefficient of $y$ in Equation 1 is 1 . So first we make $y$ the subject of Equation 1:
$y=13-3 x$
Next, substitute this expression for $y$ in Equation 2 and solve for $x$ :
$\begin{array}{ll}5 x-2(13-3 x)=7 & \text { Multiply out bracket } \\ 5 x-26+6 x=7 & \text { Combine like terms ( } x \text { 's on one side, numbers on the other) } \\ 11 x=33 & \text { Divide both sides by } 11 \text { to solve for } x \\ x=3 & \end{array}$
Finally, substitute the solution for $x$ into the expression for $y$ :
\begin{aligned} &y=13-3(3)=4 \\ &y=4 \end{aligned}
So the solution to the pair of simultaenous linear equations is $\mathbf{( 3 , 4 )}$.
by Platinum (143,296 points)

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