Solve the system of equations graphed on the coordinate axes below.
y, equals, x, plus, 5
y=
x+5
y, equals, minus, x, minus, 3
y=
−x−3
The solution to the system of equations can be found by finding the point where the two lines intersect on the graph.
The first equation, y = x + 5, has a y-intercept of 5 and a slope of 1 (since the coefficient of x is 1).
The second equation, y = -x - 3, has a y-intercept of -3 and a slope of -1 (since the coefficient of x is -1).
To find the point of intersection, we can set the two equations equal to each other:
x + 5 = -x - 3
Combining like terms, we get:
2x = -8
Dividing both sides by 2, we find:
x = -4
Substituting this value of x back into either equation, we can solve for y:
y = -4 + 5
y = 1
Therefore, the point of intersection is (-4, 1), which is the solution to the system of equations.