Solve the simultaneous equation: 5×-2y=14 and 2×+2y=14
To solve this system of equations, we can use the method of elimination or substitution.
Method 1: Elimination
We want to eliminate one variable by adding or subtracting the two equations. We notice that if we add the two equations, the term "-2y + 2y" cancels out:
5× - 2y = 14
+ 2× + 2y = 14
-----------------
7× = 28
Divide both sides by 7:
× = 4
Now we can substitute this value into one of the equations to find y. Let's use the first equation:
5× - 2y = 14
5(4) - 2y = 14
20 - 2y = 14
Subtract 20 from both sides:
-2y = -6
Divide both sides by -2:
y = 3
Therefore, the solution to the system of equations is: x = 4, y = 3.
Method 2: Substitution
We can solve one equation for one variable and substitute that expression into the other equation to eliminate that variable. Let's solve the second equation for y:
2× + 2y = 14
2y = 14 - 2×
y = 7 - ×
Now we can substitute this expression into the first equation:
5× - 2y = 14
5× - 2(7 - ×) = 14
Distribute the negative sign:
5× - 14 + 2× = 14
Simplify:
7× = 28
We get the same result as before: × = 4. To find y, we substitute again:
y = 7 - ×
y = 7 - 4
y = 3
Therefore, the solution to the system of equations is: x = 4, y = 3.
To solve the simultaneous equations, follow these steps:
Step 1: Rearrange one of the equations to solve for one variable in terms of the other.
Let's rearrange the second equation, 2x + 2y = 14, to solve 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.
Replace x in the first equation, 5x - 2y = 14, with (7 - y):
5(7 - y) - 2y = 14
Step 3: Simplify and solve for y.
35 - 5y - 2y = 14
-7y = 14 - 35
-7y = -21
y = -21 / -7
y = 3
Step 4: Substitute the value of y into either of the original equations to solve for x.
Using the second equation, 2x + 2y = 14:
2x + 2(3) = 14
2x + 6 = 14
2x = 14 - 6
2x = 8
x = 8 / 2
x = 4
Therefore, the solution to the simultaneous equations 5x - 2y = 14 and 2x + 2y = 14 is x = 4 and y = 3.