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NOW . ANSWER THE FOLLOWING PICTURE
pair of linear equation in two variables
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✨EXPERT , GENIUS
QUESTION FROM SHINING STAR ....✨✨
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Answers & Comments
Thanks for A2A
To solve the system of equations, we can use either the substitution method or the elimination method. Let's go through both of them.
Substitution Method:
In this method, we solve one of the equations for one variable and then substitute the expression obtained into the other equation.
Given equations:
2x + 3y = 11 ...(i)
2x - 4y = -24 ...(ii)
Step 1: Solve equation (i) for x:
2x = 11 - 3y
x = (11 - 3y) / 2 ...(iii)
Step 2: Substitute the value of x from equation (iii) into equation (ii):
2((11 - 3y) / 2) - 4y = -24
Cancel out the 2 in the numerator and denominator:
11 - 3y - 4y = -24
Combine like terms:
11 - 7y = -24
Step 3: Move constant terms to one side and variable terms to the other side:
-7y = -24 - 11
-7y = -35
Step 4: Solve for y:
y = -35 / -7
y = 5
Step 5: Substitute the value of y back into equation (iii) to find x:
x = (11 - 3 * 5) / 2
x = (11 - 15) / 2
x = -4 / 2
x = -2
So, the solution to the first system of equations is x = -2 and y = 5.
Elimination Method:
In this method, we add or subtract the equations to eliminate one variable.
Given equations:
x + y = 25 ...(iv)
50x + 100y = 2000 ...(v)
Step 1: Multiply equation (iv) by 50 to make the coefficients of x in both equations the same:
50(x + y) = 50 * 25
50x + 50y = 1250 ...(vi)
Step 2: Subtract equation (vi) from equation (v) to eliminate x:
(50x + 100y) - (50x + 50y) = 2000 - 1250
Simplify:
50y = 750
Step 3: Solve for y:
y = 750 / 50
y = 15
Step 4: Substitute the value of y back into equation (iv) to find x:
x + 15 = 25
x = 25 - 15
x = 10
So, the solution to the second system of equations is x = 10 and y = 15.