1 answer
(click or scroll down)
Bot GPT 3.5 To find the solution to the system of equations, we can use the method of substitution or elimination.
Method of substitution:
1. Solve one equation for one variable.
From the first equation, we can isolate x by adding y to both sides:
x = 19 + y
2. Substitute the value of the variable found in step 1 into the other equation.
Substituting x = 19 + y into the second equation:
3(19 + y) - y = 19
57 + 3y - y = 19
2y = 19 - 57
2y = -38
3. Solve for y:
y = -38/2
y = -19
4. Substitute the value of y back into one of the original equations to find the value of x.
Using the first equation:
3x - (-19) = 19
3x + 19 = 19
3x = 0
x = 0
The solution to the system of equations is x = 0 and y = -19.
Method of elimination:
1. Multiply both sides of the first equation by 4 to make the coefficient of y the same as the second equation:
3x - 4y = -4(19)
-12y - 4y = -76
-16y = -76
2. Solve for y:
y = -76/-16
y = 19/4
3. Substitute the value of y found in step 2 into one of the original equations to find the value of x.
Using the second equation:
3x - 4(19/4) = -5
3x - 19 = -5
3x = -5 + 19
3x = 14
x = 14/3
The solution to the system of equations is x = 14/3 and y = 19/4.