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, we can set the two equations equal to each other and solve for x.

Starting with the given equations:

y = -x + 7 ...(equation 1)
y = 4x - 3 ...(equation 2)

Setting equation 1 equal to equation 2:

-x + 7 = 4x - 3

Next, we can add x to both sides of the equation, and subtract 7 from both sides:

7 - 3 = 4x + x

Simplifying:

4 = 5x

Finally, we can divide both sides by 5 to solve for x:

x = 4/5

Now, we can substitute this value of x back into either equation 1 or equation 2 to find the corresponding value of y. Let's use equation 1:

y = -(4/5) + 7

Simplifying:

y = -(4/5) + 35/5

y = (35-4)/5

y = 31/5

Therefore, the estimated intersection point of the graphs is (4/5, 31/5).