Solveing using the addition method
-5x-9y=19
8x-7y=-9
1st times 8 ----> -40x - 72y = 152
2nd times 5 ----> 40x - 35y = -45
add them
- 107y = 107
y = -1
back into 1st:
-5x + 9 = 19
-5x = 10
x = -2
We can solve x or y, so I'll pick y. Let's get rid of x by multiplying the top equation by 8 and the bottom equation by 5:
8(-5x - 9y = 19)
5(8x - 7y = -9)
-40x - 72y = 152
40x - 35y = -45
---------------
.... -107y = 107
.........y = -1
I'll let you take it from here to figure out the value of x. Check solutions with the original equations. It always helps to check your work!
I hope this will help get you started.
To solve the given system of equations using the addition method, follow these steps:
Step 1: Multiply the first equation by 8 and the second equation by -5 to make the coefficients of x in both equations the same.
-5x * 8 = -40x
-9y * 8 = -72y
19 * 8 = 152
8x * -5 = -40x
-7y * -5 = 35y
-9 * -5 = 45
The equations become:
-40x - 72y = 152
-40x + 35y = 45
Step 2: Now, add the two equations together. The x terms will cancel out.
(-40x - 72y) + (-40x + 35y) = 152 + 45
Combine like terms:
-40x - 40x - 72y + 35y = 197
Simplify:
-80x - 37y = 197
Step 3: Divide the resulting equation by -1 to make the coefficient of x positive:
(-80x - 37y) ÷ -1 = 197 ÷ -1
This gives you:
80x + 37y = -197
Now, you have a new equation: 80x + 37y = -197.
Step 4: Use this new equation along with one of the original equations to eliminate one of the variables. In this case, let's eliminate y.
We will use the new equation and the first equation:
-5x - 9y = 19
80x + 37y = -197
Multiply the first equation by 37 and the second equation by 9 to make the coefficients of y the same.
-5x * 37 = -185x
-9y * 37 = -333y
19 * 37 = 703
80x * 9 = 720x
37y * 9 = 333y
-197 * 9 = -1773
The equations become:
-185x - 333y = 703
720x + 333y = -1773
Step 5: Add the two equations together. The y terms will cancel out.
(-185x - 333y) + (720x + 333y) = 703 + (-1773)
Combine like terms:
-185x + 720x - 333y + 333y = -1070
Simplify:
535x = -1070
Step 6: Divide both sides of the equation by 535 to solve for x:
535x ÷ 535 = -1070 ÷ 535
x = -2
Step 7: Substitute the value of x back into one of the original equations to solve for y. We will use the first equation:
-5x - 9y = 19
-5(-2) - 9y = 19
10 - 9y = 19
Step 8: Solve for y:
-9y = 19 - 10
-9y = 9
Divide both sides of the equation by -9:
y = 9 ÷ -9
y = -1
Solution:
The solution to the system of equations is x = -2 and y = -1.