Question

solve each system by elimination.

1. ( x + y = 4 )

( -4x - y = -1 )

Explanation:

Step1: Add the two equations

We have the system:

$$
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$$

Adding the left - hand sides and the right - hand sides of the two equations: \((x + y)+(-4x - y)=4+(-1)\)
Simplify the left - hand side: \(x + y-4x - y=(x-4x)+(y - y)=-3x\)
Simplify the right - hand side: \(4-1 = 3\)
So we get the equation \(-3x=3\)

Step2: Solve for x

Divide both sides of the equation \(-3x = 3\) by \(-3\): \(x=\frac{3}{-3}=-1\)

Step3: Substitute x into one of the original equations to solve for y

Substitute \(x = - 1\) into the first equation \(x + y=4\)
We have \(-1 + y=4\)
Add 1 to both sides of the equation: \(y=4 + 1=5\)

Answer:

The solution of the system is \(x=-1,y = 5\) (or the ordered pair \((-1,5)\))