# Solve the following systems of linear equations

3x – 2y = 4

-3x + 5y = -7

Last updated date: 28th Mar 2023

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Answer

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Hint: There are many ways to solve a system of linear equations . You can directly solve them using algebra or draw them on graphs. One of the many ways is to add one equation to the other.

Complete step-by-step answer:

We have the first equation,

3x – 2y = 4, let us call it equation 1

and

-3x + 5y = -7, equation 2

Now add equation 2 to equation 1

$ \Rightarrow $ $3x - 2y + \left( { - 3x + 5y} \right) = 4 + \left( { - 7} \right)$

$ \Rightarrow $ 3y = -3

$ \Rightarrow $ y = -1

And putting the value of y in any one of these two equations

We get ,

3x + 2 = 4

$ \Rightarrow $ $x = \dfrac{2}{3}$

Note: A system of linear equations is when we have two or more linear equations working together . This question could also be done by substitution of variables and also by constructing a graph.

Complete step-by-step answer:

We have the first equation,

3x – 2y = 4, let us call it equation 1

and

-3x + 5y = -7, equation 2

Now add equation 2 to equation 1

$ \Rightarrow $ $3x - 2y + \left( { - 3x + 5y} \right) = 4 + \left( { - 7} \right)$

$ \Rightarrow $ 3y = -3

$ \Rightarrow $ y = -1

And putting the value of y in any one of these two equations

We get ,

3x + 2 = 4

$ \Rightarrow $ $x = \dfrac{2}{3}$

Note: A system of linear equations is when we have two or more linear equations working together . This question could also be done by substitution of variables and also by constructing a graph.

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