how do you use the substitution method to solve the linear system?
-2x-5y=7
7x=y=-8
Is the second line supposed to be 7x + y = -8, or 7x - y = -8? You sweem to have inserted a second equal sign by mistake.
Whichever it is, use the second equation to derive an equation for y in terms of x. Then substitute that "y" value into the first equation, and it will be an equation in x only. Solve it.
7x+y=-8
i don't understand what you mean. could you possibly do an example?
We have this:
How do you use the substitution method to solve the linear system?
-2x - 5y = 7...Equation A
7x - y = -8...Equation B
The idea is to isolate y OR x (your choice) and then plug that into EITHER Equation A or B (your choice).
I will isolate y in Equation B.
7x - y = -8...Equation B
-y = -7x - 8
y = (-7x - 8)/-1
y = 7x + 8
Do you see that we NOW know that y is 7x + 8?
To find x, I will plug 7x + 8 into EITHER Equation A or B.
I will choose Equation A.
-2x-5y = 7...Equation A
-2x - 5(2x + 8) = 7
-2x - 10x - 40 = 7
-12x - 40 = 7
-12x = 7 + 40
-12x = 47
x = 47/-12
x = -47/12...Value for x.
We just found the value of x and it is
-47/12. See it above?
We now plug our value for x into EITHER Equation A or B to find the value of y.
I will choose Equation A again.
-2x -5y = 7...Equation A
-2(-47/12) - 5y = 7
47/6 - 5y = 7
-5y = -47/6 + 7
-5y = -5/6
y = -5/6 divided by -5
y = 1/6
The solution for this system of linear equations in two variables is
x = -47/12 and y = 1/6.
We can also write the solution this way:
(-47/12, 1/6) = (x, y), where x represents -47/12 and y represents 1/6.
Done!
whats the answer to -2x-5y=7
7x+y=-8
To solve a linear system of equations using the substitution method, we follow these steps:
Step 1: Choose one equation to solve for one variable. In this case, let's choose the second equation to solve for y.
From the second equation, we have:
7x + y = -8
Rearranging the equation to isolate y, we subtract 7x from both sides:
y = -8 - 7x
Step 2: Substitute the expression for the solved variable (y) in the other equation(s). In our case, we substitute -8 - 7x for y in the first equation.
The first equation is:
-2x - 5y = 7
Let's substitute -8 - 7x for y:
-2x - 5(-8 - 7x) = 7
Step 3: Simplify and solve the resulting equation to find the value(s) of the remaining variable(s). In our case, we solve for x.
Distribute the -5 across the parentheses:
-2x + 40 + 35x = 7
Combine like terms:
33x + 40 = 7
Subtract 40 from both sides:
33x = -33
Divide both sides by 33:
x = -1
Step 4: Substitute the found value of the variable (x) back into one of the original equations to solve for the other variable. Let's substitute x = -1 into the second equation:
7(-1) + y = -8
Simplify:
-7 + y = -8
Add 7 to both sides:
y = -1
Therefore, the solution to the linear system is x = -1 and y = -1.