Use elimination to solve the system of equations. 2x+5y=112𝑥+5𝑦=11 4x+3y=1

Step 1: Write down the system of equations

The system of equations is:

2x + 5y = 11 4x + 3y = 1

Step 2: Multiply the equations by necessary multiples such that the coefficients of x or y in both equations will cancel out each other

We can multiply the first equation by 2 to make the coefficient of x in the first equation the same as the coefficient of x in the second equation:

4x + 10y = 22 4x + 3y = 1

Step 3: Subtract the second equation from the first

Subtracting the second equation from the first gives:

7y = 21

Step 4: Solve for y

Dividing both sides of the equation by 7 gives:

y = 3

Step 5: Substitute y = 3 into the first equation

Substituting y = 3 into the first equation gives:

2x + 5*3 = 11 2x + 15 = 11 2x = 11 - 15 2x = -4

Step 6: Solve for x

Dividing both sides of the equation by 2 gives:

x = -2

So, the solution to the system of equations is x = -2, y = 3.