Answer:
Explanation:
To solve the system of linear equations by elimination:
1. Start with the given equations:
y - x = 2
y = -1/4x + 7
2. Rewrite the second equation in standard form to make it easier to eliminate variables:
y = -1/4x + 7
1/4x + y = 7
3. Multiply both sides of the second equation by 4 to eliminate the fractions:
4 * (1/4x + y) = 4 * 7
x + 4y = 28
4. Now we have the system of equations:
y - x = 2
x + 4y = 28
5. To eliminate the x variable, multiply the first equation by -1:
-1 * (y - x) = -1 * 2
-y + x = -2
6. Add the modified first equation to the second equation:
(-y + x) + (x + 4y) = -2 + 28
-y + x + x + 4y = 26
-y + 5y = 26
4y = 26
7. Divide both sides of the equation by 4 to isolate y:
4y/4 = 26/4
y = 6.5
8. Substitute the value of y back into the first equation to find the value of x:
6.5 - x = 2
-x = 2 - 6.5
-x = -4.5
x = 4.5
So, the solution to the system of linear equations is:
x = 4.5
y = 6.5
Please note that these values of x and y satisfy both equations of the system