y=7-x, 2x-y=8
To solve the system of equations y=7-x and 2x-y=8, we can use the method of substitution. Here's how:
1. Start with the first equation: y = 7 - x.
2. Substitute this expression for y in the second equation. So, instead of having y in the equation, we will have 7 - x.
2x - (7 - x) = 8.
3. Simplify the equation by removing the parentheses.
2x - 7 + x = 8.
4. Combine like terms.
3x - 7 = 8.
5. Add 7 to both sides of the equation to isolate 3x.
3x = 15.
6. Divide both sides of the equation by 3 to solve for x.
x = 5.
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the first equation:
y = 7 - x,
y = 7 - 5,
y = 2.
Therefore, the solution to the system of equations y=7-x and 2x-y=8 is x = 5 and y = 2.