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Solve the following system of equations by elimination. What is the value of x?{2x−5y=1{−3x+2y=−18 A) x = -1.5B) x = 1.5C) x = 8D) x = -8

Answer :

Given:

[tex]2x-5y=1[/tex][tex]-3x+2y=-18[/tex]

Required:

We need to find the value of x.

Explanation:

Consider the equation

[tex]2x-5y=1[/tex]

Multiply both sides of this equation by 2.

[tex]2(2x-5y)=2\times1[/tex][tex]4x-10y=2[/tex]

Consider the equation

[tex]-3x+2y=-18[/tex]

Multiply both sides of this equation by 5.

[tex]5(-3x+2y)=5(-18)[/tex][tex]-15x+10y=-90[/tex]

[tex]Add\text{ }4x-10y=2\text{ and -}15x+10y=-90.[/tex][tex]4x-10y-15x+10y=2-90[/tex][tex]4x-15x=-88[/tex][tex]-11x=-88[/tex]

Divide both sides of the equation by (-11).

[tex]-\frac{11x}{-11}=-\frac{88}{-11}[/tex][tex]x=8[/tex]

Final answer:

[tex]x=8[/tex]

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