graph the 2 lines, find the solution to the system\ny = 2x + 5\n2y = -x

Explanation:

Step1: Rewrite the second - equation

Rewrite $2y=-x$ as $y =-\frac{1}{2}x$.

Step2: Find the intersection point by substitution

Substitute $y = 2x + 5$ into $y=-\frac{1}{2}x$. So, $2x + 5=-\frac{1}{2}x$. Add $\frac{1}{2}x$ to both sides: $2x+\frac{1}{2}x+5 = 0$. Combine like - terms: $\frac{4x + x}{2}+5=0$, $\frac{5x}{2}=-5$. Multiply both sides by $\frac{2}{5}$: $x=-2$.

Step3: Find the value of y

Substitute $x = - 2$ into $y = 2x+5$. Then $y=2\times(-2)+5=-4 + 5=1$.

Answer:

The solution to the system is $x=-2,y = 1$ (the point $(-2,1)$). To graph $y = 2x+5$, the y - intercept is 5 and the slope is 2. For $y=-\frac{1}{2}x$, the y - intercept is 0 and the slope is $-\frac{1}{2}$. The two lines intersect at the point $(-2,1)$.