Question

Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5. Find the solution to both equations.

(1 point)
The intersection point is ().

Answer 1

The solution to both equations can be found by finding the x-coordinate and y-coordinate of the intersection point of the two graphs.

To find the intersection point, we can set the two equations equal to each other:

4x + 3y = 15
y = x + 5

Substituting the expression for y from the second equation into the first equation, we have:

4x + 3(x + 5) = 15

Expanding and simplifying:

4x + 3x + 15 = 15
7x + 15 = 15
7x = 0
x = 0/7
x = 0

Now substitute the value of x back into one of the original equations to solve for y:

y = 0 + 5
y = 5

Therefore, the solution to both equations is (0, 5).