Question

Solve the following system of equations 2x+3y=20 -2x+y=4

a) (1,3)
b) (3,6)
c) (2,5)
d (1,6)

Answer 1

To solve the system of equations 2x+3y=20 and -2x+y=4, we can use the method of elimination. Multiply the second equation by 2 to eliminate the x term. Add the equations to obtain a new equation. Add the equations again and solve for y, then substitute the value of y into one of the original equations to solve for x. The solution is (x, y) = (1, 6).

Step-by-step explanation:

To solve the system of equations:

1. 2x+3y=20
2. -2x+y=4

We can use the method of elimination to find the values of x and y.

First, multiply the second equation by 2 to eliminate the x term:

1. 2(-2x+y) = 2(4)
2. -4x+2y = 8

Add the equations:

1. (2x+3y)+( -4x+2y) = 20+8
2. -2x+5y = 28

Now we have a new equation:

1. -2x+5y = 28
2. 2x+3y = 20

Add the equations:

1. (-2x+5y)+(2x+3y) = 28+20
2. 8y = 48

Divide both sides of the equation by 8:

1. 8y/8 = 48/8
2. y = 6

Now substitute the value of y into one of the original equations:

1. 2x+3(6) = 20
2. 2x+18 = 20
3. 2x = 2
4. x = 1

So the solution to the system of equations is (x, y) = (1, 6).