Linear Combination. 3x+5y=17 and 2x+3y=11

Answer 1

You can solve this system of two equations with two unknowns by multiplying one equation by -2 and the other by 3.

Let's multiply the first equation below by -2 and the second by 3:

3x + 5y = 17 becomes -6x - 10y = -34

2x + 3y = 11 becomes 6x + 9y = 33

Now combine these two new equations and solve for y:

-6 x - 10 y = -34

6 x + 9 y = 33

-1 y = -1

y = 1

Then use one of the original equations to find x by substituting 1 for y:

3x + 5y = 17

3x + 5*1 = 17

3x + 5 = 17

3x + 5 -5 = 17 - 5

3x = 12

3x/3 = 12/3

x = 4

The solution for this system of equations is x = 4 and y =1

These values are the solutions for both of the original equations:

3x + 5 y = 17 3*4 + 5 *1 = 12 + 5 = 17

2x + 3y = 11 2*4 + 3*1 = 8 + 3 = 11