Solve the system of linear equations by substitution. Check your solution. y=2x+3 y=3x+5

Question

Solve this by substituting.

Answer 1

subtract the 1st equation from the 2nd.

that gives

y-y=3x-2x +5-3

0=x+2

now, subtract 2 from both sides to isolate x

-2=x or x=-2

now plug that into either of the original equations

such as y=2x+3

giving y=2(-2)+3 =-4+3=-1

x=-2, and y=-1

the solution (x,y) is (-2,-1)

check the answer by plugging that solution into the other equation y=3x+5 =3(-2)+5=-6+5=-1. it works. y=-1

another way to solve this is graph both equations, and find where they intersect. The intersection point will be the point (-2,-1)

Graph of 1st has y-intercept of 3 and slope 2. 2nd has y-intercept of 5 and slope 5. Even a very rough sketch of the graph shows an intersection where both x and y are negative. A careful sketch gives you the answer.