Step-by-step explanation:
To solve this system of linear equations, you can use the method of substitution or elimination. Let's use the elimination method:
Given equations:
1. \( 5x - 2y = 6 \)
2. \( x - 2y = -2 \)
Let's subtract the second equation from the first equation to eliminate \( y \):
\[ (5x - 2y) - (x - 2y) = 6 - (-2) \]
\[ 5x - 2y - x + 2y = 6 + 2 \]
\[ 4x = 8 \]
Now, divide both sides by 4:
\[ x = 2 \]
Now that we have \( x \), let's substitute it into either of the original equations to find \( y \). Let's use the second equation:
\[ 2 - 2y = -2 \]
Now, solve for \( y \):
\[ -2y = -2 - 2 \]
\[ -2y = -4 \]
\[ y = 2 \]
So, the solution to the system of equations is \( x = 2 \) and \( y = 2 \).
Answer: x = 2, y = 2 or (2, 2)
Step-by-step explanation:
We will solve the given system of equations for x and y.
Given:
5x - 2y = 6
x - 2y = -2
Get opposite leading coefficients by multiplying everything in the first equation by -1:
-5x + 2y = -6
x - 2y = -2
"Add" the equations together:
-5x + 2y = -6
x - 2y = -2
-------------------------
-4x = -8
Divide both sides of the equation by -4:
x = 2
Solve for y by substituting this value of x back into the equation:
5x - 2y = 6
5(2) - 2y = 6
Multiply:
10 - 2y = 6
Subtract 10 from sides of the equation:
- 2y = -4
Divide both sides of the equation by -2:
y = 2
The solution is x = 2 and y = 2, or (2, 2).