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Solve the system by substitution. 5x+2y=5 y=(-2x+3

User Imodin
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1 Answer

6 votes

Answer:

(x, y) = (-1, 5)

Explanation:

You want to solve this system of equations by substitution.

  • 5x +2y = 5
  • y = -2x +3

Substitution

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

x +6 = 5 . . . . . . . . . . simplify

x = -1 . . . . . . . . . subtract 6

y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

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Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

4x -y = 3 ⇒ y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

Solve the system by substitution. 5x+2y=5 y=(-2x+3-example-1
User SciGuyMcQ
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