Question

Saw the linear equations. Y. = X + 3 and -4x + 4y = 28

Answer 1

To solve the system of linear equations, we can use the substitution method or the elimination method.

Method 1: Substitution Method

Step 1: Solve the first equation for y in terms of x:
y = x + 3

Step 2: Substitute this expression for y in the second equation:
-4x + 4(x + 3) = 28

Step 3: Simplify and solve for x:
-4x + 4x + 12 = 28
12 = 28
This equation is not possible to solve because it results in a false statement. Therefore, there is no solution for this system of equations.

Method 2: Elimination Method

Step 1: Multiply the first equation by 4 to make the coefficients of x in both equations equal:
4(y) = 4(x + 3)
4y = 4x + 12

Step 2: Rewrite the second equation in the standard form:
-4x + 4y = 28

Step 3: Add the two equations together to eliminate x:
4y + (-4x + 4y) = (4x + 12) + 28
0 = 4x + 12 + 28
0 = 4x + 40

Step 4: Solve for x:
4x = -40
x = -10

Step 5: Substitute the value of x into either of the original equations to solve for y:
y = x + 3
y = -10 + 3
y = -7

Therefore, the solution to the system of linear equations is x = -10 and y = -7.