4. Solve the system of equations
x + y = 6
x - y = -9
add the two equations
2 x + 0 y = -3
so
x = -1.5
then
y = 6 - (-1.5) = 7.5
To solve the system of equations:
Step 1: Write down the two equations:
x + y = 6
x - y = -9
Step 2: Choose one equation and solve it for one variable in terms of the other variable. Let's choose the second equation and solve it for x:
From the second equation, we have x = -9 + y.
Step 3: Substitute the expression for x into the first equation:
(-9 + y) + y = 6
Simplify the equation:
-9 + 2y = 6
Step 4: Solve for y:
Add 9 to both sides of the equation:
2y = 6 + 9
2y = 15
Divide both sides of the equation by 2:
y = 15/2
y = 7.5
Step 5: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
x + 7.5 = 6
Subtract 7.5 from both sides of the equation:
x = 6 - 7.5
x = -1.5
Thus, the solution to the system of equations is x = -1.5 and y = 7.5.