Solve by the substitution method. 7x+3y=1 AND -4X+Y=13 What is the solution.
assistance needed
multiply the second equation, and then subtract the second equation from the first.
yes
multiply the second equation by three, sorry. Then subtract the second equation from the first.
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the second equation for y and substitute it into the first equation.
From the second equation, -4x + y = 13, we can isolate y by adding 4x to both sides of the equation:
y = 4x + 13
Now, substitute this expression for y in the first equation:
7x + 3(4x + 13) = 1
Distribute the 3 to the terms inside the parentheses:
7x + 12x + 39 = 1
Combine like terms:
19x + 39 = 1
Next, isolate x by subtracting 39 from both sides of the equation:
19x = 1 - 39
19x = -38
Now, divide both sides of the equation by 19:
x = -38/19
Simplifying further, we get:
x = -2
Now that we have the value of x, substitute it back into one of the original equations to find the value of y. Let's use the second equation:
-4(-2) + y = 13
Simplify the left side:
8 + y = 13
Subtract 8 from both sides:
y = 13 - 8
y = 5
Therefore, the solution to the system of equations is x = -2 and y = 5.