solve the simultaneous equation: 5x - 2y=14 and 2x +2y=14
To solve the simultaneous equation, we can use the elimination method:
1. Multiply the second equation by -2 to eliminate the y term:
-4x - 4y = -28
2. Add the first equation to the new equation to eliminate the y term:
5x - 2y = 14
-4x - 4y = -28
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x = -2
3. Substituting x = -2 into either of the original equations, we can solve for y:
5x - 2y = 14
5(-2) - 2y = 14
-10 - 2y = 14
-2y = 24
y = -12
So the solution to the simultaneous equation is x = -2, y = -12.
impatient much?
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Repeated postings will not get faster or better responses.
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To solve a system of simultaneous equations, we can use either the substitution method or the elimination method. I will explain both methods to help you understand.
Method 1: Substitution Method
Step 1: Solve one equation for one variable.
Let's solve the second equation, 2x + 2y = 14, for x:
2x = 14 - 2y
x = (14 - 2y)/2
x = 7 - y
Step 2: Substitute the value of x from Step 1 into the other equation.
Substitute x = 7 - y into the first equation, 5x - 2y = 14:
5(7 - y) - 2y = 14
35 - 5y - 2y = 14
35 - 7y = 14
Step 3: Solve for y.
Subtract 35 from both sides of the equation:
-7y = 14 - 35
-7y = -21
y = (-21)/(-7)
y = 3
Step 4: Substitute the value of y into x = 7 - y.
x = 7 - 3
x = 4
Therefore, the solution to the simultaneous equations is x = 4 and y = 3.
Method 2: Elimination Method
Step 1: Multiply one or both equations by a constant to make the coefficients of one of the variables opposite in sign.
In this case, we will multiply the first equation, 5x - 2y = 14, by 2 to make the coefficient of y opposite.
2(5x - 2y) = 2(14)
10x - 4y = 28
Step 2: Add or subtract the equations to eliminate one variable.
Add the new equation, 10x - 4y = 28, to the second equation, 2x + 2y = 14:
(10x - 4y) + (2x + 2y) = 28 + 14
12x = 42
Step 3: Solve for x.
Divide both sides by 12 to isolate x:
x = 42/12
x = 3.5
Step 4: Substitute the value of x into one of the original equations.
Let's substitute x = 3.5 into the second equation, 2x + 2y = 14:
2(3.5) + 2y = 14
7 + 2y = 14
Step 5: Solve for y.
Subtract 7 from both sides of the equation:
2y = 14 - 7
2y = 7
y = 7/2
y = 3.5
Since x = 3.5 and y = 3.5, the solution to the simultaneous equations is x = 3.5 and y = 3.5.
You can check the solution by substituting the values of x and y back into both equations to ensure they hold true.