how to solve symultanious equations

First, rewrite the equations so y is on it's own.

 

\(5x+2y=-2\)

 

\(2y=-2-5x\)

 

\(y=\frac{-2-5x}{2}\)

 

\(3x-5y=17.4\)

 

\(-5y=17.4-3x\)

 

\(y=\frac{17.4-3x}{-5}\)

Because both equations are equal to y, we can say they are equal to each other and solve for x.

 

\(\frac{-2-5x}{2}=\frac{17.4-3x}{-5}\)

 

\(10+25x=34.8-6x\)

 

\(31x=24.8\)

 

\(x=0.8\)

 

Then subsitute this value for x into either of the original equations to find the value of y.

 

\(y=\frac{-2-5(0.8)}{2}\)

 

\(y=-3\)

 

So x = 0.8 and y = -3