Question

Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4. Find the solution to both equations.

The intersection point is (__).

Answer 1

To find the solution to the system of equations, we can solve it using either the substitution method or the elimination method.

Let's use the elimination method:

First, we need to eliminate one variable by manipulating the equations.

We can do this by multiplying the first equation by 3 and the second equation by 1:

3(x - 5y) = 3(7)
1(3x - 2y) = 1(-4)

This simplifies to:
3x - 15y = 21
3x - 2y = -4

Now, let's subtract the second equation from the first equation:
(3x - 15y) - (3x - 2y) = 21 - (-4)
-13y = 25

Dividing both sides by -13:
y = -25/13

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

Using the first equation, we have:
x - 5(-25/13) = 7
x + 125/13 = 7
x = 7 - 125/13
x = (91 - 125)/13
x = -34/13

Therefore, the solution to the system of equations is x = -34/13 and y = -25/13.

The intersection point of the two graphs is (-34/13, -25/13).