Answer:
Explanation:
To solve the system of equations using substitution, we need to substitute one equation into the other. Let's start with the given equations:
Equation 1: y = -3x + 4
Equation 2: y = 4x - 10
We can substitute Equation 1 into Equation 2 by replacing y in Equation 2 with -3x + 4:
4x - 10 = -3x + 4
Now we can solve this equation to find the value of x. Let's isolate the x term by adding 3x to both sides:
4x + 3x - 10 = 4
Simplifying the equation gives us:
7x - 10 = 4
Next, we'll isolate the constant term by adding 10 to both sides:
7x - 10 + 10 = 4 + 10
Simplifying further gives us:
7x = 14
Finally, we can solve for x by dividing both sides of the equation by 7:
x = 14/7
Simplifying this expression gives us:
x = 2
Now that we have the value of x, we can substitute it back into either Equation 1 or Equation 2 to find the value of y. Let's use Equation 1:
y = -3(2) + 4
y = -6 + 4
y = -2
Therefore, the solution to the system of equations is x = 2 and y = -2.
In summary, to solve a system of equations using substitution:
1. Choose one equation and solve it for one variable in terms of the other variable.
2. Substitute this expression into the other equation, replacing the corresponding variable.
3. Solve the resulting equation to find the value of the remaining variable.
4. Substitute the found value back into one of the original equations to find the value of the other variable.
5. Verify the solution by substituting the values of x and y into both equations and confirming that they satisfy both equations.