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 (___).
To solve for the intersection point of the system of equations x - 5y = 7 and 3x - 2y = -4, we can use the substitution or elimination method.
Substituting the value of x from the first equation into the second equation, we get:
3(7 + 5y) - 2y = -4
21 + 15y - 2y = -4
13y = -25
y = -25/13
Now, substituting the value of y back into the first equation to solve for x:
x - 5(-25/13) = 7
x + 125/13 = 7
x = 7 - 125/13
x = 91/13
Therefore, the intersection point of the two linear equations is (91/13, -25/13).
wrong
To find the intersection point of the system of equations x - 5y = 7 and 3x - 2y = -4, we can solve using the elimination method.
First, we can multiply the first equation by 2 and the second equation by 5 to eliminate y:
2(x - 5y) = 2(7)
5(3x - 2y) = 5(-4)
This simplifies to:
2x - 10y = 14
15x - 10y = -20
Now, we can subtract the first equation from the second equation to solve for x:
15x - 2x = -20 - 14
13x = -34
x = -34/13
Substitute the value of x back into the first equation to solve for y:
-34/13 - 5y = 7
-34/13 - 7 = 5y
-195/13 = 5y
y = -195/13 * 1/5
y = -39/13
Therefore, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is x = -34/13 and y = -39/13. The intersection point is (-34/13, -39/13).