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 Question from rana, a student: solve the simultaneous equations a)3x=7y 12y=5x-1

Hi Rana,

One way you can approach this pair of equations is to solve the first equation for $x$ by multiplying each side of the first equation by $\large \frac13 .$ This results in

$x = \frac73 y.$

At this point substitute this value of $x$ into the second equation and solve for $y.$ As you can see this involves working with fractions. If you would rather not work with fractions then there is a second approach.

If you look at the two original equations you will see that the coefficient of $x$ in the first equation is 3 and the coefficient of $x$ in the second equation is 5. Multiply both sides of the first equation by 5 to get

$15 x = 35 y.$

Multiply both sides of the second equation by 3 and the coefficient of $x$ in the second equation will be 15. Substitute $15 x = 35 y$ into the second equation and solve for $y.$

Penny

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