if 3x + 5y = 2 and 2x - 6y = 20 what is 5x - y

Linear equations in two variables are solved to obtain the values of variables. Thus, the value of the equation [tex]5x - y[/tex] is [tex]\bold{22}[/tex].

Given equations are mentioned below:

[tex]3x + 5y = 2\\2x - 6y = 20[/tex]

We need to determine the values of the expression [tex]5x - y[/tex].

For calculating the value of the above expression, first we need the value of the variables x and y.

How to calculate the values of the variables?

The solution of linear equation in two variables can be calculated by different methods such as substitution, elimination and graphical methods.
Here, in this question we used substitution method to calculate the desired value.

Calculations:

[tex]\begin {aligned}3x + 5y &= 2\\3x&=2-5y\\x&=\dfrac{2-5y}{3} \end{aligned}[/tex]

Now, substitute the value of the x in another expression and solve it further.

[tex]\begin{aligned}2 \times \dfrac{2-5y}{3} -6y&=20\\ \dfrac{4-10y}{3}-6y&=20\\4-10y-18y&=60\\28y&=-56\\y&=-2 \end{aligned}[/tex]

Now, calculate the value of x.

[tex]\begin{aligned}x&=\dfrac{2-5 \times -2}{3}\\&=\dfrac{12}{3}\\&=4 \end{aligned}[/tex]

Now, calculating the value of [tex]5x - y[/tex].

[tex]5\times4 - (-2)=22[/tex]

Hence, the value of the expression [tex]5x - y[/tex] is 22.

Learn more about the linear equations in two variables here:

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