Question

Solve the following system by elimination. Show work and explain each step.

3x+y=13
4x-3y=13

please help!

Answer 1

The solution of the system of linear equation provided is (4, 1).

Explanation:

A system of linear equation can be solved using the elimination method. In this method we either add or subtract the two equations to eliminate one of the variables.

If addition or subtraction cannot be applied directly then multiply one or both the equation with a constant such that the coefficient of one of the variables becomes equal for both the equations.

The equations provided are:

`3x+y=13....(i)\\4x-3y=13....(ii)`

Addition or subtraction cannot be applied directly to eliminate any of the two variables.

Multiply equation (i) by 3,

`3(3x+y)=3*13\\9x+3y=39....(iii)`

Add equations (ii) and (iii),

`4x-3y=13\\+9x+3y=39`

Solving by eliminating the variable y,

`13x=52\\x=(52)/(13) \\=4`

The value of variable x is 4.

Now substitute the value of
`x=4` in equation (i) and solve for
`y`,

`3x+y=13\\(3*4)+y=13\\12+y=13\\y=1`

Thus, the solution of the system of linear equation provided is (4, 1).