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. (1 point) The intersection point is (
3, -2)
WRONG
Apologies for the mistake. To find the solution to both equations, we can solve the system using the method of substitution or elimination.
First, let's solve the system using the method of substitution:
1. Solve one equation for one variable in terms of the other.
From the first equation, we have:
x - 5y = 7
x = 7 + 5y
2. Substitute the expression for the variable in the second equation.
Substituting x = 7 + 5y into the second equation, we get:
3(7 + 5y) - 2y = -4
21 + 15y - 2y = -4
13y = -25
y = -25/13
3. Substitute the value of y back into one of the original equations to find the corresponding value of x.
Using the first equation:
x - 5(-25/13) = 7
x + 125/13 = 7
x = 7 - 125/13
x = 91/13
Therefore, the solution to the system of equations is x = 91/13 and y = -25/13.
what is The intersection point
Apologies for the confusion. The intersection point refers to the point at which the two lines represented by the equations intersect. In this case, the intersection point is the solution to the system of equations.
To find the intersection point, we can solve the system of equations. Here's how:
1. Let's write the system of equations:
Equation 1: x - 5y = 7
Equation 2: 3x - 2y = -4
2. We can solve the system of equations using the method of substitution or elimination. Let's use the method of elimination here:
Multiply Equation 1 by 3 and Equation 2 by -1 to eliminate x:
3(x - 5y) = 3(7)
-1(3x - 2y) = -1(-4)
Simplifying, we get:
3x - 15y = 21
-3x + 2y = 4
3. Add the two equations together to eliminate x:
(3x - 15y) + (-3x + 2y) = 21 + 4
-13y = 25
4. Solve for y:
y = 25/(-13)
y = -25/13
5. Substitute the value of y back into one of the original equations to find the corresponding value of x. Let's use Equation 1:
x - 5(-25/13) = 7
x + (125/13) = 7
x = 7 - (125/13)
x = 91/13
Therefore, the intersection point, or the solution to the system of equations, is (91/13, -25/13).
bruh wrong
Apologies for the mistake. Let's solve the system of equations correctly:
Equation 1: x - 5y = 7
Equation 2: 3x - 2y = -4
To solve the system using the method of elimination:
1. Multiply Equation 1 by 3 and Equation 2 by 1 to eliminate the x term:
3(x - 5y) = 3(7)
3x - 15y = 21
1(3x - 2y) = 1(-4)
3x - 2y = -4
2. Subtract the second equation from the first equation:
(3x - 15y) - (3x - 2y) = 21 - (-4)
-15y + 2y = 25
-13y = 25
y = -25/13
3. Substitute the value of y back into one of the original equations to find the corresponding value of x. Let's use Equation 1:
x - 5(-25/13) = 7
x + (125/13) = 7
x = 7 - (125/13)
x = 91/13
Therefore, the intersection point, or the solution to the system of equations, is (91/13, -25/13).