Solve the following simultaneous equation by substitution method 5x+y=35 & 3x-2y=14
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5 x + y = 35 Subtact 5 x to both sides
5 x + y - 5 x = 35 - 5 x
y = 35 - 5 x
3 x - 2 y = 14
3 x - 2 ( 35 - 5 x ) = 14
3 x - 2 * 35 - 2 * ( - 5 x ) = 14
3 x - 70 + 10 x = 14
13 x - 70 = 14 Add 70 to bopth sides
13 x - 70 + 70 = 14 + 70
13 x = 84 Divide both sides by 13
13 x / 13 = 84 / 13
x = 84 / 13
y = 35 - 5 x
y = 35 - 5 * 84 / 13
y = 35 - 420 / 13
y = 35 * 13 / 13 - 420 /13
y = 455 / 13 - 420 / 13
y = 35 / 13
Solution:
x = 84 / 13 , y = 35 / 13
To solve the simultaneous equation using the substitution method, we will solve one equation for one variable and substitute it into the other equation.
Let's solve the first equation for y:
5x + y = 35
Rearrange the equation to solve for y:
y = 35 - 5x
Now, substitute this value of y into the second equation:
3x - 2(35 - 5x) = 14
Expand the brackets:
3x - 70 + 10x = 14
Combine like terms:
13x - 70 = 14
Add 70 to both sides:
13x = 14 + 70
13x = 84
Divide both sides by 13:
x = 84/13
x ≈ 6.46 (rounded to two decimal places)
Now substitute this value of x back into the equation we found for y:
y = 35 - 5x
y = 35 - 5(6.46)
y = 35 - 32.3
y ≈ 2.7 (rounded to one decimal place)
Therefore, the solution to the simultaneous equations is approximately x ≈ 6.46 and y ≈ 2.7.
To solve the given simultaneous equation using the substitution method, we will solve one equation for one variable and substitute this expression into the other equation.
Let's start with the first equation:
Equation 1: 5x + y = 35
Solve this equation for y:
y = 35 - 5x
Now, substitute this expression for y into the second equation:
Equation 2: 3x - 2y = 14
Substituting the value of y, we get:
3x - 2(35 - 5x) = 14
Expand and simplify the equation:
3x - 70 + 10x = 14
13x - 70 = 14
Next, isolate the variable x. Add 70 to both sides of the equation:
13x = 14 + 70
13x = 84
Now, divide both sides of the equation by 13 to solve for x:
x = 84/13
x = 6.46 (rounded to two decimal places)
Now that we know the value of x, we can substitute it back into Equation 1 to solve for y:
5x + y = 35
5(6.46) + y = 35
32.3 + y = 35
Subtract 32.3 from both sides of the equation:
y = 35 - 32.3
y = 2.7 (rounded to one decimal place)
Therefore, the solution to the simultaneous equation 5x + y = 35 and 3x - 2y = 14 is x = 6.46 and y = 2.7.