Question
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
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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