Let's solve for x. x + 4 y = ( 14 ) ( 3 ) x + 7 y Step 1: Add -42x to both sides. x + 4 y + − 42 x = 42 x + 7 y + − 42 x − 41 x + 4 y = 7 y Step 2: Add -4y to both sides. − 41 x + 4 y + − 4 y = 7 y + − 4 y − 41 x = 3 y Step 3: Divide both sides by -41. − 41 x − 41 = 3 y − 41 x = − 3 41 y Answer: x = − 3 41 y
Solve the system of linear equations with substitution;
x+4y=14 Equation 1 <span>
3x+7y=22 Equation 2
Solve Equation 1 for x
x + 4y = 14 Isolate the variable by moving the second variable to the other side using the inverse operation which in this case is subtraction. So..... x + 4y = 14 <span> - 4y = -4y </span> x = 14 - 4y
42 - 5y = 22 Combine like terms and remember the 12 is -42 -42 technically negative -5y = -20 Isolate the variable which in this case we divide -5y/-5 = -20/-5 y = 4
Going back to Equation 1. Insert the know variable to solve for x.
x+4y=14 Equation 1
x + 4(4) = 14 x + 16 = 14 Isolate the variable by subtracting 16 from both sides - 16 -16 x = -2
The solution is an ordered pair (x,y) ........ (-2, 4).
Check your work by inserting the ordered pair into either of the equations.