Question

Solve the systems of equations
3x + y = 2
7x - 4y = 30

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Answer 1

To solve this system of equations, we can use either the substitution method or the elimination method.

Let's use the elimination method:

1. Multiply the first equation by 4, and the second equation by 1 to make the coefficients of y the same.

4(3x + y) = 4(2)
1(7x - 4y) = 1(30)

This gives us:
12x + 4y = 8
7x - 4y = 30

2. Add the two equations together to eliminate y:

12x + 4y + 7x - 4y = 8 + 30
19x = 38
x = 38 / 19
x = 2

3. Substitute x back into one of the original equations to find y. Let's use the first equation:

3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

Therefore, the solution to the system of equations is (2, -4).