Question

What is the solution for this system of equations y=2/5x+4 y=2x+12

Answer 1

The solution to the system of linear equations y = 2/5x + 4 and y = 2x + 12 is found by setting them equal to each other, simplifying, and solving for x, which gives x = -5. Substituting this back into either equation yields y = 2.

Step-by-step explanation:

Solving a System of Linear Equations

To solve the system of equations y = 2/5x + 4 and y = 2x + 12, we need to find a value of x that satisfies both equations simultaneously. Since both equations are equal to y, we can set them equal to each other to find x:

1. 2/5x + 4 = 2x + 12
2. Subtract 2/5x from both sides: 4 = 2x - (2/5)x + 12
3. Find a common denominator and combine like terms: 4 = (10/5)x - (2/5)x + 12
4. Simplify: 4 = (8/5)x + 12
5. Subtract 12 from both sides: 4 - 12 = (8/5)x
6. -8 = (8/5)x
7. Multiply both sides by 5/8 to solve for x: x = -5

Now that we have x, we can substitute it back into either of the original equations to find y:

1. y = 2(-5) + 12
2. y = -10 + 12
3. y = 2

The solution to the system of equations is x = -5 and y = 2.