`x + 2y = 1, 5x - 4y = -23` Solve the system of linear equations and check any solutions algebraically.

Expert Answers

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EQ1:  `x + 2y = 1`

EQ2: `5x-4y=-23`

To solve this system of equation, let's apply substitution method. So let's isolate the x in the first equation.

`x + 2y = 1`

`x = 1 - 2y`

Then, plug-in this to the second equation.

`5x - 4y=-23`

`5(1-2y) - 4y = -23`

And solve for y.

`5-10y-4y=-23`

`5-14y=-23`

`-14y=-23-5`

`-14y=-28`

`y=(-28)/(-14)`

`y=2`

Now that the value of y is known, let's solve for x. Plug-in y=2 to the first equation.

`x+2y = 1`

`x + 2(2)=1`

`x+4=1`

`x=1-4`

`x=-3`

Therefore, the solution is (-3,2).

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