Question

solve each system by graphing2) y=4x + 3y= -x - 23) y= - 1/2x - 1y = 1/4x - 44) y = -1 y = -5/2x + 45) y = 3x - 4y = -1/2x + 36) y = -2x + 2y = -2x - 27) y = 5x -2y = 5x - 2

Answer 1

2)

x=-1

y=-1

Explanation

when you have a system of 2 equations and 2 variables ( x and y ), to solve the systme graph each line and the point where the lines intersect each other is the solution

$\begin{gathered} y=4x+3\text{ Equation(1)} \\ y=-x-2\text{ Equation(2)} \end{gathered}$

Step 1

graph equation 1 (green)

find two points

a) when x= 0

$\begin{gathered} y=4x+3 \\ y=4\cdot0+3 \\ y=0+3 \\ y=3 \\ \text{the coordinate is (0,3)} \end{gathered}$

b) when x= 2

$\begin{gathered} y=4x+3 \\ y=4\cdot2+3 \\ y=8+3 \\ y=11 \\ \text{the coordinate is (2,11)} \end{gathered}$

now, draw a line that passes thougth the points (0,3) and (2,11)

Step 2

now, do the same for equation (2)(blue)

when x=0

$\begin{gathered} y=-x-2 \\ y=0-2 \\ y=-2 \\ \text{the coordinate is (0,-2)} \end{gathered}$

when x=2

$\begin{gathered} y=-x-2 \\ y=-2-2 \\ y=-4 \\ \text{the coordinate is (2,-4)} \end{gathered}$

now, draw a line that passes thougth the points (0,-2) and (2,-4).(blue line)

the answer is the point where the lines intersect each other so, the answer is

$\begin{gathered} (-1,-1) \\ or \\ x=-1 \\ y=-1 \end{gathered}$

I hope this helps you