Question

solve the system of linear equations by graphing.
y = -5x + 3
y = 2x - 4
the solution is (□, □).

Explanation:

Step1: Analyze the first equation \(y = -5x + 3\)

To graph this line, we can find two points. When \(x = 0\), \(y = -5(0)+3 = 3\), so we have the point \((0, 3)\). When \(y = 0\), \(0=-5x + 3\), solving for \(x\) gives \(x=\frac{3}{5}=0.6\), so we have the point \((0.6, 0)\).

Step2: Analyze the second equation \(y = 2x - 4\)

For this line, when \(x = 0\), \(y = 2(0)-4=-4\), giving the point \((0, -4)\). When \(y = 0\), \(0 = 2x - 4\), solving for \(x\) gives \(x = 2\), so we have the point \((2, 0)\).

Step3: Find the intersection point

The solution to the system of linear equations is the point where the two lines intersect. By graphing the two lines (either by plotting the points we found or using the slope - intercept form \(y=mx + b\) where \(m\) is the slope and \(b\) is the y - intercept), we can see that the two lines intersect at the point \((1, -2)\). We can also verify this algebraically by setting the two equations equal to each other:

$$
LATEXBLOCK0
$$

Substitute \(x = 1\) into \(y = 2x-4\), we get \(y=2(1)-4=-2\).

Answer:

\((1, -2)\)