Question

Estimate the intersection point of the graphs of the following linear equations in two variables.
y=-x+7
y=4x-3

Answer 1

To find the intersection point of the graphs of these two linear equations, we need to solve the system of equations formed by setting the two equations equal to each other:

-y + 7 = 4x - 3

We can rearrange this equation to solve for y:

y = 4x + 3

Now we have a system of equations:

y = -x + 7
y = 4x + 3

To solve this system, we can set the two expressions for y equal to each other:

-x + 7 = 4x + 3

Now we can solve for x:

7 - 3 = 4x + x
4 = 5x
x = 4/5

Substituting this value of x back into one of the original equations, we can solve for y:

y = -4/5 + 7
y = 35/5 - 4/5
y = 31/5

Therefore, the intersection point of the graphs of the two linear equations is (4/5, 31/5).