3x + 4y = -14
3x − 10y = 14
Subtract first equation from second to solve for y. Work it from there.
To solve this system of equations, you can use the method of substitution or elimination. I will explain how to solve it using the substitution method.
Step 1: Choose one equation and solve for one variable in terms of the other variable.
Let's solve the first equation, 3x + 4y = -14, for x:
3x = -14 - 4y
x = (-14 - 4y) / 3
Step 2: Substitute the expression for x in the second equation.
Replace x in the second equation, 3x - 10y = 14, with the expression we found in step 1:
3((-14 - 4y) / 3) - 10y = 14
Step 3: Simplify the equation.
Multiply both sides of the equation by 3 to eliminate the fraction:
-14 - 4y - 10y = 42
Step 4: Simplify further.
Combine like terms:
-14 - 14y = 42
Step 5: Move the variables to one side and the constants to the other side.
Add 14 to both sides:
-14y = 56
Step 6: Solve for y.
Divide both sides by -14:
y = -56 / 14
y = -4
Step 7: Substitute the value of y into one of the original equations to solve for x.
Let's use the first equation, 3x + 4y = -14:
3x + 4(-4) = -14
3x - 16 = -14
Step 8: Solve for x.
Add 16 to both sides:
3x = 2
Divide both sides by 3:
x = 2/3
So the solution to the system of equations is x = 2/3 and y = -4.