I have tried these problem cannot get the answer so could some one help me.
Solve by the subsitution method.
2x-7y=-11
2x +17=y
What is the solution of the system.
I have tried to work those problem all I ask is for your help
the second equation tells you exactly what y is
y = 2x+17
put that into the first:
2x - 7(2x+17) = -11
I am sure you can finish that.
Once you have the x, sub that back into your
y = 2x + 17
To solve the system of equations using the substitution method, we will solve one equation for one variable and then substitute that expression into the other equation.
1. Start with the first equation: 2x - 7y = -11.
2. Solve the second equation for one variable. The second equation is: 2x + 17 = y. We can rewrite this equation as y = 2x + 17 by subtracting 2x from both sides.
3. Substitute the expression for y from step 2 into the first equation. Replace y with 2x + 17 in the equation 2x - 7y = -11:
2x - 7(2x + 17) = -11.
4. Simplify the equation:
2x - 14x - 119 = -11.
Combine like terms:
-12x - 119 = -11.
5. Add 119 to both sides of the equation to isolate the variable:
-12x - 119 + 119 = -11 + 119.
Simplify:
-12x = 108.
6. Divide both sides of the equation by -12 to solve for x:
x = 108 / -12 = -9.
7. Substitute the value of x = -9 back into the second equation to find y:
y = 2x + 17 = 2(-9) + 17 = -18 + 17 = -1.
8. Therefore, the solution to the system of equations is x = -9 and y = -1.
Just a note: The substitution method helps us solve systems of linear equations where we can express one variable in terms of the other and then substitute it back into the equation. This method allows us to find the values of the variables that satisfy both equations in the system.