Question

Use elimination to solve each system of equations.4x + y = 233x - y = 12Use elimination to solve each system of equations.4x + y = 233x - y = 12

Answer 1

The solution is (5, 3)

Step-by-step explanation

To use elimination method, we have to subtract (or add) one equation from the other, in order to eliminate one of the variables. Then we'll have one equation with one variable. We solve it for that variable and then replace into one of the equations of the system to solve for the eliminated variable.

In these equations, we have +y in the first one and -y in the second one. We can add both equations to eliminate y:

`\begin{gathered} (4x+y)+(3x-y)=23+12 \\ 4x+3x+y-y=35 \\ 7x=35 \end{gathered}`

Solving for x:

`\begin{gathered} 7x=35 \\ x=(35)/(7) \\ x=5 \end{gathered}`

Now, we have to replace x = 5 into one of the equations and solve for y. Replacing in the first equation:

`\begin{gathered} 4x+y=23 \\ 4\cdot5+y=23 \\ 20+y=23 \\ y=23-20 \\ y=3 \end{gathered}`

The solution to this system is (5, 3)