if I solve this by substitution
8x+7y=-13
x=29-7y
I end up with -3.8
But I think there is no solution
sub the 2nd into the 1st
8(29-7y) + 7y = -13
232 - 56y + 7y = -13
-49y = -245
y = 245/49 = 5
then x = 29 - 7(5) = -6
You should have questioned your "no solution" answer, since the lines have different slopes. The have to intersect somewhere.
To solve the system of equations using substitution, you need to follow these steps:
1. Take one of the equations and solve it for one variable. In this case, the second equation gives you the value of x in terms of y: x = 29 - 7y.
2. Substitute the expression for x from Step 1 into the other equation. Replace all instances of x in the first equation with the expression 29 - 7y.
So, the first equation becomes: 8(29 - 7y) + 7y = -13.
3. Simplify and solve for y. Distribute 8 through the parentheses: 232 - 56y + 7y = -13. Combine like terms: -49y + 232 = -13.
4. Solve for y: -49y = -13 - 232. Simplify: -49y = -245. Divide by -49: y = -245/-49, which simplifies to y = 5.
5. Substitute the value of y back into one of the original equations to solve for x. From the second equation, substitute y = 5: x = 29 - 7(5) = 29 - 35 = -6.
So the solution to the system of equations is x = -6 and y = 5.
Now, let's check your result of -3.8 by substituting it into both equations:
For the first equation: 8(-3.8) + 7(5) = -30.4 + 35 = 4.6.
For the second equation: -3.8 = 29 - 7(5) = 29 - 35 = -6.
As you can see, -3.8 does not satisfy both equations simultaneously. Therefore, you are correct in concluding that there is no solution to this system of equations.