Question

find the solution to the system by graphing (use a blank graph in noteability or graph paper)
( y = x + 3 )
( -4x + y = -3 )
hint: solve the second equation for y to get into y=mx+b format
(1, 3)
(5, 2)
(-4, -3)
(2, 5)

Explanation:

Step1: Rewrite the second equation

The second equation is \(-4x + y = -3\). Solve for \(y\) by adding \(4x\) to both sides: \(y = 4x - 3\).

Step2: Set the two equations equal

We have \(y = x + 3\) and \(y = 4x - 3\). Set them equal: \(x + 3 = 4x - 3\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(3 = 3x - 3\). Add 3 to both sides: \(6 = 3x\). Divide by 3: \(x = 2\).

Step4: Find \(y\)

Substitute \(x = 2\) into \(y = x + 3\): \(y = 2 + 3 = 5\). So the solution is \((2, 5)\).

Answer:

(2, 5)