7x-4y=-10
4y=x-2
add the two equations to each other and you will get rid of y so you can solve for x
or
substitute (x-2) for 4 y in the first equation
did you just type in any random letters you saw?
To solve this system of equations, we can use the method of substitution. Here's how we can do it:
1. Start with the first equation: 7x - 4y = -10.
2. To solve for x, isolate x by moving the term with y to the other side of the equation. Add 4y to both sides of the equation:
7x = 4y - 10.
3. Divide both sides of the equation by 7 to isolate x:
x = (4y - 10) / 7.
4. Now, we substitute this expression for x in the second equation: 4y = x - 2.
Replace x with (4y - 10) / 7 in the second equation:
4y = ((4y - 10) / 7) - 2.
5. Simplify the equation. Start by distributing the 1/7 to the terms inside the parenthesis:
4y = (4y/7) - (10/7) - 2.
6. Combine like terms on the right side of the equation:
4y = (4y/7) - (24/7).
7. To get rid of the fractions, we can multiply every term in the equation by the least common denominator (7 in this case). This will cancel out the denominators:
4y * 7 = 4y - 24.
8. Simplify the equation further:
28y = 28y - 168.
9. Subtract 28y from both sides of the equation:
28y - 28y = -168.
10. The variable y has canceled out, which means the equation is an identity. This indicates that the two equations are dependent, and there are infinitely many solutions. In this case, there is no unique solution.
Therefore, the system of equations 7x - 4y = -10 and 4y = x - 2 has no unique solution.