Solve the simultaneous equation: 5×-2y=14 and 2×+2y=14

Answer 1

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.