Find the value x which satisfies the following simultaneous equations: 2x + 5y = 18 3x + 4y = 20

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Answer to a math question Find the value x which satisfies the following simultaneous equations: 2x + 5y = 18 3x + 4y = 20

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Esmeralda

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To find the value of x that satisfies the simultaneous equations: Equation 1: 2x + 5y = 18 Equation 2: 3x + 4y = 20 We can solve this system of equations using the method of substitution or elimination. Let's use the method of elimination: Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the x terms: Equation 1: 6x + 15y = 54 Equation 2: 6x + 8y = 40 Now, subtract Equation 2 from Equation 1: (6x + 15y) - (6x + 8y) = 54 - 40 6x - 6x + 15y - 8y = 14 7y = 14 Divide both sides of the equation by 7: 7y/7 = 14/7 y = 2 Now, substitute the value of y back into either Equation 1 or Equation 2. Let's use Equation 1: 2x + 5y = 18 2x + 5(2) = 18 2x + 10 = 18 2x = 18 - 10 2x = 8 Divide both sides of the equation by 2: 2x/2 = 8/2 x = 4 Therefore, the value of x that satisfies the given simultaneous equations is x = 4.

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