Where do the graphs of the following equations intersect??
X+y=5
2×+2y=10
Is it 0,5
the equations are the same line
multiply the 1st one by 2 , and you get the 2nd one
I'm not sure I understand
To find the intersection point of the graphs of the given equations, we can solve the system of equations by using the method of substitution or elimination.
Let's solve it using the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, X + y = 5, we can rewrite it as X = 5 - y.
Step 2: Substitute the expression of one variable into the other equation.
Substituting X = 5 - y into the second equation, 2X + 2y = 10, we get:
2(5 - y) + 2y = 10.
Simplifying this equation:
10 - 2y + 2y = 10,
10 = 10.
Step 3: Analyze the equation.
Since 10 = 10, the equation is true for any value of y. This means that the two equations represent the same line, and they intersect at all points along that line.
Therefore, the graphs of the equations X + y = 5 and 2X + 2y = 10 intersect at infinite points along the line represented by the equations. So, there isn't a single intersection point, but rather a whole line of points.