Question

practice exercises lesson 7.3b
solve the system of equations using the addition/elimination method.
$x + y = 1$
$x - y = 3$
$\bigcirc$ $(0, 1)$
$\bigcirc$ $(3, 0)$
$\bigcirc$ $(2, -1)$
$\bigcirc$ $(-3, 4))

Explanation:

Step1: Add the two equations

Add the equations \(x + y = 1\) and \(x - y = 3\) together. This gives \((x + y)+(x - y)=1 + 3\). Simplifying the left side, \(y\) and \(-y\) cancel out, so we have \(2x=4\).

Step2: Solve for x

Divide both sides of \(2x = 4\) by 2. So, \(x=\frac{4}{2}=2\).

Step3: Substitute x into one equation

Substitute \(x = 2\) into the first equation \(x + y = 1\). We get \(2 + y = 1\).

Step4: Solve for y

Subtract 2 from both sides of \(2 + y = 1\). So, \(y=1 - 2=-1\).

Answer:

\((2, -1)\)