solve by the elimination method
5x+5y= -7
7x-3y=19
The solution is (___,___)
Please help I am lost on how to work and complete this one.
Manipulate the equations so you can eliminate one variable.
One way would be to multiply the first equation by 3, and the second equation by 5. Always do this for BOTH SIDES of the equations.
15x + 15y = -21
35x - 15y = 95
Now add them and the y term is eliminated.
50x = 74
x = 37/25
Use any of the equations with x and y to solve for y. It looks like a rather messy fractional answer.
Check my work; I'm sloppy
I see where and how you can up with 50x=74 but where did the x=37/25 come from that confuses me.
Thank you for your help
50x = 74
Divide both sides of the equation by 50.
x = 74/50 = 37/25
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To solve this system of equations using the elimination method, follow these steps:
Step 1: Choose one of the variables to eliminate. In this case, let's eliminate the variable "y".
Step 2: Multiply one or both of the equations by a constant so that the coefficients of the variable chosen in step 1 are opposite in the two equations. In this case, we'll multiply the first equation by 3 and the second equation by 5 to make the coefficients of "y" opposite.
Equation 1: 5x + 5y = -7 (multiply by 3)
Equation 2: 7x - 3y = 19 (multiply by 5)
The new equations become:
Equation 1: 15x + 15y = -21
Equation 2: 35x - 15y = 95
Step 3: Add the two equations together to eliminate the variable "y".
(15x + 15y) + (35x - 15y) = (-21) + 95
50x = 74
Step 4: Solve for x by dividing both sides of the equation by 50.
x = 74 / 50
x = 1.48
Step 5: Substitute the value of x back into one of the original equations to solve for y. Let's use Equation 1:
5x + 5y = -7
5(1.48) + 5y = -7
7.4 + 5y = -7
5y = -7 - 7.4
5y = -14.4
y = -14.4 / 5
y = -2.88
Therefore, the solution to the system of equations is (1.48, -2.88).