can someone explain step by step to do math problems for to solve the system ill use an example 7x3y=-2 -7x-7x=14
correct the typo in 7x3y=-2
type each equation in a new line, so we tell where one ends and the next one begins.
7x3y=-2
-7x7x=14
this is worse than before, now I have to read it as
21xy = -2
-49x^2 = 14
it can't be that, since the second equation clearly has no real solution.
I have a feeling you meant to type
7x + 3y = -2
-7x + 7y = 14
but until you clarify the equation, there is no point in working it out.
7x + 3y = -2
-7x + 7y = 14
To solve the system of equations 7x + 3y = -2 and -7x - 7y = 14, you can use the method of elimination. Here is a step-by-step explanation:
Step 1: Write down the two equations.
7x + 3y = -2 (Equation 1)
-7x - 7y = 14 (Equation 2)
Step 2: Choose one variable to eliminate by multiplying one of the equations by a suitable factor so that the coefficients of that variable in both equations are the same or differ only by a sign.
In this case, the x-terms have opposite coefficients (-7x and 7x). To eliminate the x-term, we need to make the coefficients the same. To do this, multiply Equation 1 by -1:
-1 * (7x + 3y) = -1 * (-2)
-7x - 3y = 2 (Equation 3)
Step 3: Add Equation 2 and Equation 3 together to eliminate the x-term.
(-7x - 7y) + (-7x - 3y) = 14 + 2
-14x - 10y = 16 (Equation 4)
Step 4: Simplify Equation 4 if possible. Divide the entire equation by -2 to make the coefficient of x positive.
(14x + 10y) / -2 = 16 / -2
7x + 5y = -8 (Equation 5)
Step 5: Now, you have a new system of equations:
7x + 5y = -8 (Equation 5)
-7x - 7y = 14 (Equation 2)
Step 6: Notice that the x-terms in Equation 5 and Equation 2 have opposite coefficients (-7x and 7x). Add Equation 5 and Equation 2 together to eliminate the x-term.
(7x + 5y) + (-7x - 7y) = -8 + 14
-2y = 6
Step 7: Solve for y by dividing both sides by -2.
y = -3
Step 8: Substitute the value of y back into either of the original equations to solve for x. Let's use Equation 1:
7x + 3(-3) = -2
7x - 9 = -2
Step 9: Solve for x by adding 9 to both sides of the equation.
7x = -2 + 9
7x = 7
Step 10: Divide both sides of the equation by 7 to solve for x.
x = 1
Step 11: The solution to the system of equations is x = 1 and y = -3.
By following these step-by-step instructions, you can solve the given system of equations.