Answer:
Explanation:
To find the number of solutions for a system of linear equations, we can use the method of substitution or elimination. Here, we'll use the method of substitution.
We'll start by solving for x in one of the equations and then substitute that expression into the other equation. If the resulting equation has a unique solution, then the system has a unique solution. If the resulting equation has no solution, then the system has no solution. If the resulting equation has infinitely many solutions, then the system has infinitely many solutions.
Let's start by solving the first equation for x:
y = -7/2 x + 11
To solve for x, we'll isolate x by subtracting 11 from both sides of the equation:
y - 11 = -7/2 x + 11 - 11
y - 11 = -7/2 x
Next, we'll multiply both sides of the equation by -2/7 to cancel out the fraction on the right side:
-2/7 (y - 11) = -2/7 (-7/2 x)
-2/7 y + 22/7 = 7/2 x
Now, we have an expression for x in terms of y. We can substitute this expression into the second equation:
7x + 2y = 20
7 (-2/7 y + 22/7) + 2y = 20
Substituting -2/7 y + 22/7 for x, we get:
7 (-2/7 y + 22/7) + 2y = 20
Expanding the left side of the equation, we get:
-2y + 22 + 2y = 20
0y = -2
Since 0y is never equal to -2, this equation has no solution.
Therefore, the system of equations has no solution, and there are no values of x and y that satisfy both equations simultaneously.
So, the system of equations y = -7/2 x + 11 and 7x + 2y = 20 has no solutions.