Solve each linear equation by substitution. The answer is suppose to be (-2, -4) Thank you for your help.
{-5x+3y=10
x-4y=14
i need help on the steps can somebody put the answer step by step please
To solve a system of linear equations by substitution, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation for x:
x - 4y = 14
x = 14 + 4y
2. Substitute the expression from step 1 into the other equation.
Replace x in the first equation with (14 + 4y):
-5(14 + 4y) + 3y = 10
3. Solve the resulting equation for the remaining variable.
-70 - 20y + 3y = 10
-17y = 80
y = -80/17 (the y-coordinate)
4. Substitute the value of y back into one of the original equations to solve for the other variable.
Let's substitute y = -80/17 into the second equation:
x - 4(-80/17) = 14
x + 320/17 = 14
x = 14 - 320/17
x = -162/17 (the x-coordinate)
So, the solution to the system of equations is (-162/17, -80/17).
To convert the solution to whole numbers, you can multiply both coordinates by 17:
(-162/17 * 17, -80/17 * 17) = (-162, -80).
Therefore, the solution in whole numbers is (-162, -80), which is not (-2, -4).
There might be a mistake in the original problem or calculation. Please double-check.