The system of equations has an x-value solution at Response area and a y-value solution at Response area .
To find the x-value solution, we can solve one of the equations for x in terms of y and substitute it into the other equation. Let's use the first equation:
2x + 3y = 8
Solving for x, we get:
2x = 8 - 3y
x = (8 - 3y) / 2
Now we substitute this expression for x into the second equation:
3x - 5y = 13
3((8 - 3y) / 2) - 5y = 13
Simplifying this equation, we get:
12 - 9y - 5y = 26
Combine like terms:
-14y = 14
Divide both sides by -14:
y = -1
Now we can substitute this value of y into the first equation to find the x-value solution:
2x + 3(-1) = 8
2x - 3 = 8
2x = 11
x = 11/2
So, the x-value solution is 11/2 and the y-value solution is -1.
To find the solution to the system of equations, you will need to solve for the values of x and y.
To solve for x, we can use the first equation. Rearrange it to isolate x:
2x + 3y = 12
Subtract 3y from both sides:
2x = 12 - 3y
Now divide both sides by 2:
x = (12 - 3y) / 2
This gives us the expression for x in terms of y.
To solve for y, we can use the second equation. Rearrange it to isolate y:
3x - 2y = 7
Subtract 3x from both sides:
-2y = 7 - 3x
Now divide both sides by -2:
y = (7 - 3x) / -2
This gives us the expression for y in terms of x.
Now that we have expressions for both x and y, we can substitute one into the other to solve for a specific value.
For example, if we substitute the expression for y into the expression for x, we can find the value of x in terms of y.
x = (12 - 3y) / 2
To find the x-value solution, substitute a value for y into this expression and calculate x.
Similarly, to find the y-value solution, substitute a value for x into the expression for y and calculate y.
By substituting values and performing the calculations, you can find the x-value and y-value solutions to the system of equations.