Question

solve the system by graphing.
4x + 2y = 2
3x = 4 - y
the solution is (□, □).

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(4x + 2y=2\), we solve for \(y\):
Subtract \(4x\) from both sides: \(2y=-4x + 2\)
Divide by 2: \(y=-2x + 1\)

For the second equation \(3x = 4 - y\), we solve for \(y\):
Add \(y\) to both sides: \(y+3x = 4\)
Subtract \(3x\) from both sides: \(y=-3x + 4\)

Step2: Find the intersection point

To find the solution of the system, we set the two equations equal to each other since at the intersection point, the \(y\) - values (and \(x\) - values) are equal:
\(-2x + 1=-3x + 4\)
Add \(3x\) to both sides: \(-2x+3x + 1=-3x + 3x+4\)
Simplify: \(x + 1=4\)
Subtract 1 from both sides: \(x=4 - 1=3\)

Now substitute \(x = 3\) into \(y=-2x + 1\):
\(y=-2(3)+1=-6 + 1=-5\)

We can also verify by substituting into \(y=-3x + 4\): \(y=-3(3)+4=-9 + 4=-5\)

Answer:

\((3,-5)\)