How do I use substitution to solve the system? Please help Addition and equal key is not working . It's asking for x equals and y equals.
-5x plus 2y equal 16
y equal 2x plus 7
-5x +2y = 16 eq'n 1
y = 2x + 7 eq'n 2
sol'n
sub eq'n2 to eq'n 1
-5x + 2(2x +7) = 16
-5x + 4y +14 = 16
-x = -14+16
x = -2 ---> sun to eq'n 2
y = 2(-2)+7
y = 3
-5x + 2y = 16
y = 2x + 7
To do substitution, choose an equation and from that equation, choose a variable and express it in terms of the other. Then substitute that expression to the other equation.
Here, let's choose the second equation.
y = 2x + 7
Then let's choose the variable, y. It's already expressed in terms of the other variable, x.
y = 2x + 7
Then substitute it to the other equation:
-5x + 2y = 16
-5x + 2(2x + 7) = 16
-5x + 4x + 14 = 16
-x + 14 = 16
-x = 16 - 14
x = -2
Now that you have a value for x, substitute it to either equation and solve for y.
To use substitution to solve the system, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable (choose whichever equation seems easier).
For example, in the second equation, rewrite it as y = 2x + 7.
2. Substitute the expression obtained in step 1 into the other equation. This will create a new equation with only one variable.
Using the first equation: -5x + 2(2x + 7) = 16.
3. Simplify and solve the new equation.
Simplifying the equation gives: -5x + 4x + 14 = 16.
Combining like terms: -x + 14 = 16.
Subtracting 14 from both sides gives: -x = 2.
Multiplying both sides by -1 gives: x = -2.
4. Substitute the value of x found in step 3 back into one of the original equations to solve for the other variable.
Using the second equation: y = 2(-2) + 7.
Simplifying: y = -4 + 7.
Therefore, y = 3.
So, the solution to the system of equations is x = -2 and y = 3.